There's a Transgender Bible? You mean I've been going about this all wrong?

I have a few points to make, but couldn't resist the joke first. Sorry.
Anyway, I get the impression that some therapists see people who are in "crisis mode". The fact that you weren't speaks very well about your frame of mind, and your competence, and I'm sure that your therapist was pleased. I have a feeling that's the source of all the positive reaction-- the therapist is initially trying to build a trusting relationship with the client, etc. Sounds like she overplayed it a bit, but I don't think I would read too much into it.
I would suggest, as you said, that you go to the second session and see where it goes. If it's more of the same, then you might consider going to see someone else. Just because a person is a gender therapist doesn't mean that they'll actually be much help to you.
You aren't, or shouldn't be, locked into seeing only that one person, so if you decide after the second session that it isn't doing much for you, go see someone else.