Hello bashfulsoul: The Skeezyks is an older person.

But I'll just mention that gender identity dysphoria is something I have struggled with all of my life. (So it seems we may have some small bit in common... except that I never did anything to address my GID issues.)
Personally, I think that many people who struggle with mental health issues wish to be of help to others who have similar struggles. It's part of the reason we're all here on PC!

(This is true of people who struggle with physical illness & disability as well.) So your interest in working with people in the LGBT community makes perfect sense to me. And it is certainly true that there is a great need for mental health professionals who are knowledgeable about, & sympathetic to, the special concerns LGBT persons have. My personal opinion is that a mental health professional who is not knowledgeable & sympathetic can do more harm than good.
Now, as to your question regarding why it is you want to do this, & if it could simply be a reflection of your idealization of your own therapist, my thinking is that this would be excellent fodder for in-depth discussions with your T. It is certainly possible that your interest is based on your idealization of your T. Or it may not be. It is even possible that it is the case but that, even so, this is still something you would very much like to do & be glad you did in years to come.

Many successful people got into doing what they did because of the influence of someone they met who was in the profession & who inspired them. But the only way to sort this all out & decide how you want to proceed is, I think, to have those in-depth discussions. There are various ways to look at this. And different ways to proceed. There is also no way to be absolutely sure. But the best way to proceed is, it seems to me, to talk it all through with someone you respect. And, from what you wrote, it sounds as though your T fits the bill, as they say.