Thanks for posting, Elliot.
Do you know if your therapist has experience with trans folks? Unless I really liked my therapist, I don't think I would come out as trans to them if they did not have this kind of experience. After all, if I'm looking for help, I don't want to have to train the person who's supposed to be helping me.
Do you have a long relationship with this therapist? Do you trust them? Your gut instincts count here.
Having a therapist experienced with gender stuff is ideal, but this isn't always possible, and sometimes you have to make your situation work for you.
It took me a few months before I could speak about being trans with anyone. I didn't have the words yet, and didn't quite know how to frame it all. Some personal work had to happen before I could share it.
Joshua