Kindergarten is not mandatory in California. If I were you, I'd consider pulling her this year and homeschool, and use that time to work on a skip to start straight into 2nd next fall. It will probably be easier to find a charter umbrella school in CA that would register her as a 1st grader right now than negotiating for a mid-year skip in a new school.
Do you have an idea of her approximate reading level and math level? When my son skipped from 1st to 2nd, we used the Iowa Acceleration Scale Manual. It took a lot of the emotion out of the decision and made it much more black and white for school staff to see. You would need IQ and achievement to use it effectively. If that doesn't work, you can also push for subject acceleration in her strongest areas.
As for using IDEA, I have had some success throwing around "free and appropriate public education." While there is no federal mandate, many school administrators don't know or understand that. You can use fancy special education law to get them to listen, but it doesn't guarantee anything.
