Ethically, it's pretty dicey for therapists to work with people they know socially -- for good reasons. That said, she may be OK with seeing you, given that your relationship with her is through your friend; she would likely want to set some boundaries around interacting with you outside of therapy. It's certainly something I'd expect to discuss with her at the outset -- if she's too casual about how it would work, that would raise red flags for me about her ethics and competence.
I think it would also depend on whether you're looking for short-term therapy with the goal of getting the diagnosis, or for something longer term.
It's worth talking to her, no matter what -- at the very least, she should be able to give you a referral to someone else, and perhaps agree to consult with that person if they need "backup" around gender issues.
Good luck!