We pick up on doctors with agendas pretty fast after we learn the basics. This is a medical condition were we have to know more that the doctor because in the end the doctor only states we are able to make the decision for ourself. We are the one who makes the final decision and all the responsibility rest in our hands. It's a moment in our life were we are altering the path of our life and if we make a mistake, we live with it for the rest of our life. If we know the city you are near, somebody will provide you with a list of therapist. If your child is seeing a Gender Therapist, you may be welcome there as well. Most often the SO don't need nearly as much therapy as we do. We have been living with this for years and it does a pretty good job of messing us up on the inside. It takes a while for us to clean up the mess.
If your child has issues with the therapist, we are willing to discuss them. I suspect the name of the therapist came from here and if so, there is a pretty good chance the person is qualified. The main reason you might want a therapist is if you are having trouble adjusting to this. In my mother case, she never saw a therapist because at first she though she could fix me. Over the years she adjusted to the fact this was going to happen and there wasn't much she could do about it. I also talked with her about myself when ever she was willing to listen so she understood a good deal about this. We are best friends and we work together tending my brothers estate.
As for the terms you call your child by, my mom used my male name for years and often I had to brush it off. Thankfully she has it right now and I haven't heard that name in years. As your child moves into the female role, it should help you see the daughter you have gained.