Don't freak out--most vets don't get every aspect of treating feline diabetes right--you're lucky that you at least have a vet that advocates home testing! Many people show up here without home testing at all and their vets charging them for useless office curves. :YMSIGH: My vet was great about advocating home testing and recommending a commercial, low carb, canned diet but she was also not having me test daily when I started out. I changed that on my own when I found out that the current minimum testing recommendation for Lantus was thrice daily testing.
Like diabetes in humans, feline diabetes is best treated at home, with routine self-adjustments to dose. Many vets don't like the idea of giving owners this sort of control over insulin dosing, but it's the best and safest way to treat the cat. What insulin are you using? I've attached an article for you to print out and give to your vet--it discusses the safety and efficacy of owner adjusted dosing via daily home testing with Lantus (glargine). I would discuss this treatment plan with your vet, and see if he will get on board with you. If he's open to doing things your way, I would stick with him. If he's not, you may need to find a vet who is willing to work with you. That is what you need--finding a vet that is up to date with every detail of feline diabetes is near impossible.
If you're using Prozinc, there's a different dosing protocol for that insulin but it's the same basic concept of adjustment via daily testing.
Also, one unit is not a "tiny" dose. 1u is an average dose--most cats on a low carb, canned diet never need much more than 1u.