Homeschooling is so different in so many different situations, I think it would largely depend on how you handled it.
Do you think your daughter will benefit from NOT interacting with other kids? Or will it let her 'avoid' the issue- but eventually she will have to go back and join her peers and the problem will still be there?
I think you need to talk extensively with her doctor before just pulling her out to homeschool her. It could be just the break she needs- or it could allow her to become even less social and retreat further into herself.
Have you talked to her teachers and admin at school? Is there some specific reason she is having such anxiety about school= social pressures, bullying, etc? Maybe just a smaller school or group of really close friends could help her more? Does she attend any type of group therapy or counseling?
Also- what are your qualifications for homeschooling? Have you taught before- do you feel confident in your ability to teach math, history, etc. to your daughter? I know you mean well, but you will have to be very well prepared to teach your daughter at home and keep her from falling behind.
There are so many different resources for homeschooling now, both educational and social that you can use. But it sounds like just that won't overcome your daughter's troubles.
Talk to the doctor- talk to your daughter about specifically WHY she thinks homeschooling will help her and how she plans to socialize, etc. if she does that. It sounds like it would not be a solution on its own, but maybe could help, but only under the right circumstances.
good luck!