Not sure that private school is the answer. You can continue to challenge her at home while she continues on at school. Supplementing the everyday work with interesting workbooks or projects may help.
You might also ask her present school if they would consider having her work with less gifted kids in math or working with younger children to help them with their math.
No, she is not there to teach other kids. that will become extremely boring very quickly. She needs to learn math, not teaching.
In general it is very, very wrong to take smart kids and turn them into teachers for less-gifted kids. It isn’t what they are there to do.