3 units is quite a large dose so you would definitely not want to change over to a lower carb diet unless you were monitoring the BSL.
We test the bsl for multiple reasons.
First of all we always test every time before we give any insulin, to make sure that it is safe to do so. You would not want to give insulin if the bsl is too low.
Then we test at different times during the cycle ( the time between one insulin dose and the next insulin dose....12 hours), to see how the insulin is affecting the bsl.
This way we can see if we are giving too much, too little or the correct amount of insulin.
When we change the dose of insulin we go up or down in 0.25 unit increments. This way it is safe and we do not go past the correct dose.
It takes time to understand it all.....no one will expect you to "get it" straight away.
And we are all willing to help you along the way. As lots of questions.
We have a spreadsheet that records all the bsl and helps to get the bigger picture. You can click onto anyone's SS which you will see in their signature at the bottom of their posts. Have a look at a few and it will give you an idea of what I mean.
When you have time it would be a good idea to set up your spreadsheet. Here are the instructions. If you are not very tech savvy, yell and someone will help you set it up....many of us needed the help!
http://www.felinediabetes.com/FDMB/threads/fdmb-spreadsheet-instructions.130337/
Do you have a good understanding vet? A lot of vets do not know a lot about feline diabetes.