I haven't read all of the responses yet because I only have a few minutes.

Generally, I think asking for this sort of information is a distraction. I know you think it will help you to feel more comfortable, knowing that your T has faced issue X. But it may also very well boomerang, undermining your trust in her competence. Personally, I always wanted a T who was emotionally healthy. While it is certainly possible for someone to have faced major trauma and recovered and become a T, there are an awful lot of Ts out there, especially with MA degrees, who are not over their own stuff, and their decisions to become Ts are more closely connected to their pursuit of their own healing than anything else. I didn't want to be their client.

A good T will respect their own limitations, based upon their self-analysis, and not work with a client on issues that have unresolved emotional resonance for themselves.

If she hasn't shown you through her actions any reason to doubt her, it would be wise to think about why you have a need for this info right now.