What happens if a patient falls in love with her doctor?

Professionalism. Depends on what type of doctor this is. It's a transference response, because the patient doesn't really know the doctor. In a psychotherapeutic relationship, it can be discussed for the patient's benefit. With non-psychiatrists, it might lead to transferring the patient to other providers. The needed processing of transference isn't usually an area of expertise in non psychiatric physicians.
Transference. Can hinder progress and needs to be dealt with in the session, or referral to another therapist.