It is not illegal in the States, but therapists are prohibited from engaging in sexual contact with clients for reasons of professional ethics mentioned by Lynn. But no, not illegal - illegal is something that YOU as a client would be at fault for, which is rather absurd. The only person at fault is the Therapist - in other words, you can try dating her and she would either explain why it is not OK, or, even discontinue you as a client. But you can ask what you want - the onus is on her. You can do whatever you want.
as far as asking her out goes.

Caveat: Unless it is different in AU.