If we want to move her to Public school would the school district accept that she is accelerated in a private school program and place her at the level equal to that or would we be forced by age to start kindergarten? (We live in Texas and I haven't found the answer to this question out on the internet.)
Run a survey: call the district offices (and the local school, too). Tell them "my daughter is in a private kindergarten and is 4 years old. She's doing very well. Will you just promote her to grade 1 if we move to the public schools next year?"
See what they say. If they say "We'll test her and see," this means they have options and they might be able to force her to repeat kindergarten. Get as much information as you can.
Then wait a few days. Ideally, get your husband or someone else to call (different voice). This person must ask "My son is in first grade in a private school but is only 5 years old. He's doing very well. We're thinking of moving to the public schools. Would you just advance him to 2nd grade?"
See what they say. From what I've read/heard, schools are more constrained once a child finishes grade one. I think it has something to do with kindergarten not being "real" school yet but 1st grade being "real" school.
Just an idea.
Val