If she's old enough to make the decision, she's old enough to do the work that comes with the decision -- finding a doctor to approve a medical exemption with no history of severe vax reactions or explaining to me why she holds a sincere religious exemption (because I will not sign off on a *religious* exemption that comes down to "don't want a shot").
Yeah, well you have pretty much trashed her decision and thrown road blocks up to her ever acting on it. You might as well march her down to the doctors and have her jabbed.
ETA: to be fair, I would do absolutely nothing to assist my 16 yo get a vaccination. They would have to make the appointment with the clinic/doctors, and get themselves there and pay for it. But then again, I wouldn't be doing anything to her body against her wishes.