This happened to us.
Girls did PreK in one state. Academically excelled and advanced. Suggested that they go on to K at 4 turning 5 by schools (instead of developmental K for Fall/Summer Bdays). Cut off date Dec. Oct Bday.
Moved.... new state. Cut off date of Sept 1st.
Had to do PreK again. No exceptions to the cut-off dates for K or 1st. No matter what. We had teacher letters, testing scores, etc. Nothing. Privates schools also followed the cut-off dates. We did a lot of 'fun' stuff at home to keep them learning! Both my DDs are reading easy chapter books, writing in journals, and doing basic math. It has been nice to have the freedom to explore their interests- we have learned all the different states of the US! They love it and that is not something we would have had time for if they were in school all day or is it part of the K programming.
If they had done K in 1st state, they would have had to repeat it.
This year they did PreK (AGAIN). The only thing they got out of it was friends (1/2 day program) and they enjoy it since it is play based.
Our solution to next year is to place them in a K/1 split classroom. They will technically be 'K' kids, but can work at a K/1 (or higher) level. The school has splits for most grades so we could enjoy this set up for awhile. Starting in 1st they also have Gifted programming (pull out once a week). After that we will have to do 1st grade, and we will see where they are at. Starting in 2nd kids sometimes 'skip' grades that are older and/or redshirted or just missed cut-off dates.
I am not happy with having to do PreK again, but am thrilled that they can do 1st/2nd grade work in a K(ish) setting.
Your options woudl likely be:
2. talk to the local schools- she what they offer, they may be willing to put her in K adn then maybe move up later in the year and/or offer a K/1 split like we are doing. See if they have gifted/advanced programming
3. Find a private school that would offer a scholarship and/or some allowances on cut-off
4. Plead your case to the local school board (done K, have a teacher letter suggesting 1st)
If you get a choice of school districts (like we did) in picking housing for varying districts. Talk to a bunch of principals & local teachesr. visit the schools. See what they can do for you. I know the school we are going to send our girls to is willing to work with us (them) and another district was not. We could have chosen to find housing in either area. Guess which area we picked?
Good Luck. It is very frustrating.