In reference to the possibly moving at the end of the year and probably to another state (I'm assuming) your plan to accelerate her and worry about it all next year might benefit you. Lots of states have rules set up for acceleration through the private schools from the same state and not accepting this unless they have finished 1st grade in the private sector. But the loophole is finishing kindergarten in the private sector in another state. For some reason they allow them to enter in 1st grade and not repeat kindergarten regardless if they were in public or private. So if you do move to one of these states your DD will be allowed into 1st grade with no problem.

Crossing my fingers for you. It does sound promising that the school will at least consider it, especially since your daughter will just turn 4 this month. Most schools wouldn't even give you the opportunity to prove anything.