Fructosamine tests are helpful in diagnosing diabetes, but once you are testing glucose regularly at home, they are not really necessary. I actually asked for one once because I wanted it as another indicator of how things were going with Mia. The result came back within normal range, and the vet was thrilled. On the other hand, I had a lot of testing data to show that while she was getting into good numbers pretty much every cycle, she was still spending too much time in higher numbers. Her pre-shot numbers were still much higher than I wanted. To me, it was very important for her to stay under the renal threshold as much of the time as possible so that her pancreas could heal... my goal has always been remission... vets are usually just happy with decent regulation. So, I changed her insulin in spite of the good fructosamine result. Her numbers are so much better now, and I have been able to steadily decrease her insulin dosage.
It really looks like your baby needs more insulin. You have not found the 'break through' dose yet. I don't know what good a fructosamine would do you at this point. You know she is staying too high. Do you want to pay for a test to confirm what you already know?