Should I stay in the room while my daughter gets her first pelvic exam?

Depends. It all depends on what your daughter wants. If your presence calms her it is very apropiate. The earlier the girls age the more likely she will need you there for the pelvic.
Only if she wants yo. A pelvic exam is embarassing for everyone and having "your mother" in the room can be embarassing or reassuring. I would leave it up to your daughter to decide. All doctors will have a chaperone in the room so nothing should happen to her if you are worried about that. If no chaperone is offered then i would absolutely stay in the room. You can always stand behind the curtain.