You may ask, it's not inappropriate, but don't be surprised if she declines to answer. Instead, she might want to explore what makes you interested. Or not. Therapists give different responses to those kinds of questions depending on what they believe would be in the best interests of the client. They may disclose some of their personal information sometimes, but, most of the time they would choose either to decline to answer without any further comments or they would decline to answer but would want to explore why this information is important to the client. As I said, it all depends on how they perceive the situation and what they believe would be in the best interests of the client. There is no general rule about this other than to use their best judgment of what would benefit the client.