Here's some thoughts. I'm new at this gifted stuff, but I'll proceed any way.
I think you should go to the gifted teacher or school psychologist and see if they get your child's abilities. After that I would go to the principal if need be. Try to work out a plan with them. It sounds like you need an individual learning plan. Get a flexible plan together on your own. Go into a meeting with an open mind to see what will work with their system. I think a calm unemotional approach works well. How can you and the school together help her? Make sure you have read some about gifted and teaching them in a regular class room.
If you can do the homeschooling but think your involvement in it would be bad, consider getting a retired or part time teacher at home. There is online education. Varing from free to expensive. A friend has her children do a free homeschooling program with a online teacher offered thru our state. Her 2nd Grader did this mostly on his own once he became oriented. He is much more content now that is is not being bothered about all the extra reviewing not needed at school.
Can you get her to do something at home that she could bring into school? Ex. My son does his extra math book after he is allowed to go ahead of class on math page. He does this work well independently so it's easy for the teacher. Could your DD try something like Alex for a month at home only $20 a month so you can show she can do it independently. These are math examples but you didn't mention if this was an area of need for enrichment/accelloration.
If the school is worried about accelloration try a baby step of just one class. You need to get them to see her ability and overcome their objections and be flexible.
Best of Luck. I would expect this to be difficult but worthwhile.
