I live in CA, but your district requirements might be different. I wonder why you put DD in public kinder when you say she did K at the Montessori. Did you not know that the age/birthday rule only applies to Kinder (at least in our district). So far as I know, there are no other restrictions on other grades like that.
I just moved our 4.5 year old from her preschool to a private preschool/pre K/K school. The Kinder is fully accredited...at the end of the year, the teacher/director will write a review and reccomendation and she will probably have to take a test to enter first, but that is our plan...
If you have a reccomendation from the previous school, especially if they are accredited, I would approach it more that you want a first grade entrance exam, not requesting IQ testing, which you are not likely to get unless they agree your child might have a learning or other disability.
