I don't think transition causes you to be happy, anymore than therapy does. It helps you to be yourself, though, and not being able to do that can make you pretty unhappy. And there's lots of reasons why depression and suicide is so common among transgender people, and transition isn't going to magically solve all those problems. You But from your post, you understand that and she doesn't.
As for waiting until 26 because of some wierd claim about brain development? I think that would be a harmful requirement. You need to transition when you're ready to, and not at some magic age she made up with no basis whatsoever. The earlier you can transition, the better it will work. I wish so much that I'd figured this out and started ten or even twenty years ago. As it is I'm just hoping for anything. That doesn't mean rush and do it before you're ready. But her telling you you have to wait if you were otherwise ready, is very wrong.
That said, going through a therapy process with a gender specialist before you begin, if that's what you need to do, is a good idea if you're able to and think you need help working it out. Regret is pretty rare, actually, and it's not like transitioning means instant irreversible surgery.
Wishing you the best of luck in this. Finding a gender therapist === very good idea. A non specialist, even a well meaning one, may not have the resources to help you. And she is definitely acting on some misconceptions.