You're making a mountain out of a mole hill. Her numbers are perfectly fine and normal for a non-D child, even if you have a reading in the 130s. The meter you use is inaccurate, you're not using a lab quality unit nor venous draw samples. People naturally swing outside of the normal range of 80-120(90-130 with the current generation of meters really, higher depending on many variables such as meds and even oxygen levels), without being considered Diabetic or even Pre-Diabetic. Blood glucose levels do not stay 100% lab parameter range all of the time. There are fluctuations in normal healthy people. Even down to where they run, high or low end of the lab normal range. The fasting numbers you're seeing in the morning is her liver preparing her for the day, so she has energy to wake up and get going - again, they are normal.
You should consult with her pediatrician, but he/she will assure you everything is fine. Even if there is a BG of 300 on your meter, a doctor will not pay heed to the parent's meter unless there are other symptoms present. Maybe you can talk them into doing a urine to check if any glucose is spilling into the urine, depending on the results(positive presence above a certain range), they might test further. They might proceed with a blood draw for A1C and a glucose tolerance test. If it spikes and then returns to normal on a glucose tolerance test, a person is still not considered Pre-Diabetic. However some people can have a serious problem with the test, even without problems with BG normally - the amount of glucose given can make a normal person spike and crash dangerously low, so it's not recommended for children usually. If BG levels spike and remain elevated, then there is an issue, but if it returns to lab normal there is not. Doctors are not going to believe you period with the numbers you're seeing, especially since the meter you use is inaccurate(all of them are). Doctors let children with Diabetes run higher because of the danger of brain and nerve damage from lows.
Really, the only way to track whether she might become Diabetic or not is to watch C-peptide levels, and IgG and IgM antibodies against insulin, not testing BG at home. Chances are you will not find a Doc willing to put a child through unnecessary testing, you have to have a valid reason. Giving blood glucose lowing meds if not indicated can expedite the process of turning to full Diabetic, that is why Docs are conservative and wait to start them. All you can do is make sure she learns how to eat right, and make sure she does stay away from wheat at all costs, especially the hidden stuff.