I just did this! My DS 14 is in 8th, and is dealing with a back injury that the doctors can't figure out, and he has been out of school because of it on and off all year. In Illinois, all you have to do is let the school's principal know, and then notify the regional board of education. There's no reporting or review -- I don't have to tell the school district what I'm having him study, how many hours, have them review his grades, etc. He's already registered for high school, and the HS says they don't need anything else.
But -- and I'm sure you've already done this -- I'd think long and hard before pulling a child out. You're not only changing her classroom, you're removing her from friends, the extra classes (health, gym, art & music). Will she have a hard time reintegrating next year? With a 7th grader, and I know this from experience (same kid had major problems with anxiety the last two years, so he's missed a lot) they get a lot of teasing and intrusive questions when they come back. Have you talked to the school? Looked at getting tutors? Have you maybe considered having her tested to see if she has a learning disorder of some kind? If that were the case, homeschooling would not be the most effective treatment for you. In our case, it was really the only solution available to us at this time, given his physical limitations, but believe me, I'd explore every other possibility before pulling a child out, especially an older child. If you think this really may be your best situation, call and talk to the principal at your school. He/she may have some other solutions, but they'd be able to tell you what you need to do to homeschool.
Erin