Spraying glyphosate on your "greens" is not generally...

Spraying glyphosate on your "greens" is not generally recommended. They soon become "yellows", and then "browns".

As for the neonictinoids, they're hard to keep track of:
Australian Government List of Neonicotinoids

July 5, 2016

Source: https://portal.apvma.gov.au/pubcris
Image courtesy of Tony Linka.
Acetamiprid

• Acetamiprid
• Echem Acetamiprid 225 Insecticide
• Primal Insecticide
• Acetamiprid
• Defender Concentrate Maxguard Systemic, Contact & Residual Insecticide
• Defender Maxguard Systemic, Contact & Residual Insecticide Kills & Controls
• Crown 225sl Systemic Insecticide
• Intruder Insecticide
• Acetamiprid
• Supreme 225 Sl Insecticide

Clothianidin

• Clothianidin
• Dantop Systemic Insecticide
• Sumitomo Shield Systemic Insecticide
• Sumitomo Stealth Systemic Insecticide
• Sumitomo Samurai Systemic Insecticide
• Clothianidin

Thiacloprid

• Piranha Dip For Sheep
• Lineout Insecticide
• Thiacloprid
• Calypso 480 Sc Insecticide
• Imidacloprid
• 4farmers Imid-Triadimenol Seed Dressing
• 4farmers Imidacloprid 200sc Insecticide
• 4farmers Imidacloprid 600 Flowable Seed Dressing Insecticide
• Ac Impressor 350 Soil Insecticide
• Ac Impressor 600 Seed Dressing
• Accensi Imidacloprid 200 Sc Termiticide
• Accensi Imidacloprid Hose-On Lawn Insecticide
• Accensi Imidacloprid Lawn & Garden Insecticide
• Accensi Imidacloprid Ready To Use Insecticide
• Accensi Imidacloprid Turf And Ornamental Insecticide
• Accensi Rose Spray Advanced Insect, Mite & Disease Control Rtu
• Agmate Imidacloprid 600 Fs Insecticide
• Agrimart Imidacloprid 200 Insecticide
• Agro-Essence Imidacloprid 200 Sc Insecticide
• Agro-Essence Insecticide Imidacloprid 600fs
• Agrocn Imidacloprid 350 Sc Insecticide
• Agspray Aphid Guard 200 Sc Aphicide/Insecticide
• Amgrow Conquer Hose-On Lawn Insecticide
• Amgrow Conquer Lawn & Garden Insecticide
• Amgrow Conquer Ready To Use Insecticide
• Amgrow Rose Spray Advanced Ready To Use
• Amparo Seed Treatment Insecticide
• Antmaster Liquid Bait
• Apparent Imidacloprid 200 Sc Insecticide
• Apparent Imidacloprid 350 Sc Insecticide
• Apparent Imidacloprid 600 Sc Insecticide
• Arrow Plus Seed Treatment
• Avenge Pour-On Lousicide For Sheep
• Aw Inflict 600 Seed Dressing
• Imidacloprid
• Aw Irrupt 350 Soil Insecticide
• Barmac Imidaturf Turf And Ornamental Insecticide
• Baygon Fly Control Window Stickers Flower
• Bithor Water-Based Insecticide
• Blattanex Cockroach Gel Bait
• Brunnings Imidacloprid Bug Kill Systemic Insect Control
• Brunnings Lawn Grub & Beetle Kill
• Brunnings Lawn Grub & Beetle Kill Concentrate
• Chaindrite Utility Insecticide
• Choice Immi 600 Flowable Seed Dressing Insecticide
• Confederate 200 Sc Insecticide
• Confederate 350 Sc Insecticide
• Confederate 600 Flowable Seed Dressing Insecticide
• Confidor 200 Sc Insecticide
• Confidor Concentrate Insecticide
• Confidor Garden Insecticide
• Confidor Guard Soil Insecticide
• Confidor Hose-On Lawn Insecticide
• Confidor Plant Insecticide
• Confidor Ready To Use Insecticide
• Conquest Imida 600 Seed Treatment Insecticide
• Conquest Imidah 350 Sc Insecticide
• Country Imidacloprid 200 Sc Termiticide
• Couraze 200 Sc Insecticide
• Couraze Classic Insecticide
• Covert Cockroach Gel Bait
• Crop Culture Komondor 200 Sc Insecticide
• Easyfarm Imidacloprid 350 Soil Insecticide
• Echem Imidacloprid 200 Sc Insecticide
• Emerge Flowable Seed Treatment

Imidacloprid

• Enviromax Imidacloprid 200sc Termiticide & Insecticide
• Enviromax Imidacloprid 200sc Turf, Crop & Ornamental Insecticide
• Ezycrop Imidacloprid 200 Sc Insecticide
• Ezycrop Imidacloprid 350 Soil Insecticide
• Ezycrop Imidacloprid 600 Seed Treatment Insecticide
• Farmalinx Imi 200 Sc Insecticide
• Farmalinx Imi 600 Seed Dressing Insecticide
• Farmoz Dominion 200 Sc Termiticide
• Farmoz Kohinor 200 Insecticide
• Fmc Imidacloprid 600 Insecticide
• Foliarflo Plus Seed Treatment
• Forward Imidacloprid 600 Seed Dressing Insecticide
• Gaucho 350 Flowable Seed Treatment Insecticide
• Gaucho 600 Flowable Seed Treatment Insecticide
• Gaucho 600 Red Flowable Seed Treatment Insecticide
• Genero 600 Flowable Seed Dressing Insecticide
• Genfarm Imidacloprid 200sc Insecticide
• Genfarm Imidacloprid 600 Flowable Seed Dressing Insecticide
• Granular Products Imidacloprid 350 Soil Insecticide
• Guardian Seed Treatment Insecticide
• Hombre Cereal Seed Treatment
• Hombre Ultra Cereal Seed Treatment
• Hortico Imidacloprid Systemic Insect Killer
• Hortico Systemic Insect Killer Imidacloprid Concentrate
• Imidacloprid 3.5% Pour-On Lice Treatment For Sheep
• Imiforce 200sc Termiticide
• Imiforce Utility Insecticide
• Impress 350 Soil Insecticide
• Imtrade Annihilate 200 Sc All Purpose Insecticide
• Imtrade Imidacloprid 350 Sc Insecticide
• Initiator Systemic Plant Insecticide And Fertiliser
• Kenso Agcare Imi-Ken 200sc Termiticide
• Kenso Agcare Savage 200 Insecticide
• Kenso Agcare Savage 600 Flowable Seed Dressing Insecticide
• Kohinor 350 Sc Insecticide
• Masmart Imi – Flow 600 Red Seed Treatment
• Masmart Imi-Flow 200 Insecticide
• Masmart Imi-Flow 600 Seed Treatment
• Maxforce Gel Insecticide
• Maxforce Quantum Liquid Ant Bait
• Maxforce White Cockroach Gel
• Merit Turf And Ornamental Insecticide
• Mission Imidacloprid 200 Sc All Purpose Insecticide
• Mission Imidacloprid 350 Sc Insecticide
• Mortein Naturgard Fly Control Window Stickers
• Mortein Naturgard Fly Control Window Stickers Trusted Household Protection Louie The Fly
• Novaguard Imidacloprid 200 Sc Insecticide
• Novaguard Imidacloprid 350 Soil Insecticide
• Novaguard Imidacloprid 600 Seed Treatment Insecticide
• Nufarm Mallet Turf And Ornamental Insecticide
• Nufarm Nuprid 200sc Insecticide
• Nufarm Nuprid 350sc Insecticide
• Nufarm Nuprid 600 Flowable Seed Dressing Insecticide
• Nufarm Nuprid 600 Red Flowable Seed Dressing Insecticide
• Nufarm Nuprid 700wg Insecticide
• Nufarm Preface 200sc Termiticide
• Ospray Couraze 200 Sc Insecticide
• Ozcrop Imidacloprid 350 Sc Insecticide
• Ozcrop Imidacloprid 600 Fs Insecticide
• Pacific Imidacloprid 200 Sc Insecticide
• Permatek Im 30 Insecticide
• Pest Controllers Own Imidacloprid 200sc Termiticide
• Picus Seed Treatment Insecticide
• Preminator Termiticide
• Premise 200 Sc Termiticide
• Premise Foam Insecticide
• Pride Insecticide
• Proguard Plus Seed Treatment
• Proleaf Plus Seed Treatment
• Protect-Us Multiag Insecticide
• Protectaflo Seed Treatment Insecticide
• Prothor 200 Sc Termiticide
• Provado 200 Sc Insecticide
• Quickbayt Fly Bait
• Quickbayt Spray Fly Bait
• Rainbow Imidacloprid 350 Sc Insecticide
• Rainbow Imidacloprid 600 Sc Insecticide
• Relay 200 Sc Termiticide
• Rentokil Prothor 200 Sc Termiticide
• Resource Gardening Systemic Insect Control Ready To Use
• Revenge Pour-On Lice Treatment For Sheep
• Richgro Bug Killa Granular Garden Insecticide
• Roachkill Home Cockroach Gel Bait
• Rygel Imidacloprid 200 Sc Insecticide
• Sabakem Imidacloprid 350sc Soil Insecticide
• Sabakem Imidacloprid 600fs Seed Treatment Insecticide
• Searles Conguard Garden & Lawn Insecticide
• Searles Conguard Garden Insecticide
• Senator 350 Sc Insecticide
• Senator 600 Flowable Seed Treatment
• Senator 600 Red Flowable Seed Treatment
• Senator 700wg Insecticide
• Sharda Imidacloprid 600 Flowable Seed Dressing Insecticide
• Sharp Shooter Complete Bug & Insect Spray Imidacloprid
• Sharp Shooter Complete Bug & Insect Spray Imidacloprid Concentrate
• Sharp Shooter Complete Lawn Grub & Beetle Killer Hose On Imidacloprid Systemic Insecticide
• Sharp Shooter Complete Lawn Grub & Beetle Killer Imidacloprid Systemic Insecticide Concentrate
• Sherwood Imiforce 200sc Termiticide
• Silvashield Injectable Tree Insecticide
• Sindor 200 Sc Insecticide
• Sinochem Intersect 200sc Insecticide
• Smart Imidacloprid 600 Flowable Seed Dressing Insecticide
• Solfac Duo Residual Insecticide
• Sovenge 3.5% Pour-On Lice Treatment For Sheep
• Superway Imidacloprid 200 Insecticide
• Surefire Flystar Bait
• Surefire Spectrum 200sc Insecticide
• Surefire Spectrum 350 Sc Soil Insecticide
• Suscon Maxi Soil Insecticide
• Suscon Yellow Intel Insecticide
• Systemic Advanced Control Yates Rose Gun Advanced Insect, Mite & Disease Control
• Systemic Advanced Control Yates Rose Shield Advanced Insect, Mite & Disease Control
• Tanalith Ti Insecticide
• Temprid 75 Residual Insecticide
• Termatrix Termite Foam Insecticide
• Titan Imidacloprid 200 Insecticide
• Titan Imidacloprid 600 Flowable Seed Dressing Insecticide
• Trespass 350 Insecticide
• Tri-Power Seed Treatment
• Turf Culture Tirem 200sc Insecticide
• Vectothor Fly Bait
• Veteran Plus Seed Treatment
• Voodoo 200 Insecticide
• Voodoo Guard Soil Insecticide
• Yates Complete Lawn Insect Control
• Yates Confidor Lawn & Garden Insecticide
• Yates Confidor Ready To Use Insecticide
• Yates Confidor Tablets Garden Insecticide
• Zero Tolerance On Cockroaches Rentokil Advanced Cockroach Gel Bait
• Zooter 600 Seed Treatment Insecticide
• Zooter Soil Guard Insecticide
• Zorro Cereal Seed Treatment
• Advantage For Cats Over 4 Kg
• Advantage For Dogs 10 – 25 Kg
• Advantage For Dogs 4 – 10 Kg
• Advantage For Dogs Over 25 Kg
• Advantage For Kittens & Small Cats Up To 4 Kg
• Advantage For Puppies & Small Dogs Up To 4 Kg
• Advantix For Dogs 10-25kg
• Advantix For Dogs 4-10kg
• Advantix For Dogs Over 25kg
• Advantix For Puppies And Small Dogs Up To 4kg
• Advocate For Cats Over 4kg
• Advocate For Dogs 10-25 Kg
• Advocate For Dogs 4-10 Kg
• Advocate For Dogs Over 25kg
• Advocate For Kittens And Small Cats Up To 4kg
• Advocate For Puppies And Small Dogs Up To 4 Kg
• Imidacloprid 3.5% Pour-On Lice Treatment For Sheep
• Avenge Pour-On Lousicide For Sheep

Thiamethoxam

• Thiamethoxam
• Voliam Flexi Insecticide
• Resolva All-In-One Bug And Fungus Killer With Tmx Plantguard For Tomatoes
• Talon Ant Killer Gel
• Cruiser Opti Insecticide Seed Treatment
• Cruiser Extreme Insecticide Seed Treatment
• Resolva Liquid Concentrate Bug Killer With Tmx Plantguard For Your Ornamentals And Tomatoes
• Resolva Protect And Feed Bug Killer Granules With Tmx Plantguard
• Durivo Insecticide
• Resolva All-In-One Bug And Fungus Killer With Tmx Plantguard
• Optigard Ant Bait Gel
• Meridian Turf Insecticide
• Actara Insecticide
• Agita 10 Fly Bait
• Agita 100 Plus Fly Spray And Paint-On
• Cruiser 350 Fs Insecticide Seed Treatment
• Cruiser 600 Fs Insecticide Seed Treatment

Bunnings has dumped Confidor, but on precautionary grounds, saying that the evidence against it was far from being conclusive.
My suggestion is to avoid long-acting systemic insecticides, and only apply when bees and predator insects aren't around - a policy which seems to have kept my bees and mantises happy.

And since flea powders are on the list,and pyrethroids are also "bad", the dog may have to have to learn to take a daily bath.