The big difference between a psychologist and a psychiatrist, is that the latter can prescribe drugs. If you're opposed to using drugs for any issues you might be having, perhaps try telling your dad that and see if you can't agree on a psychologist. Some will be by the book and make you do three months of therapy. Both of mine have been willing to write a letter after the first meeting.
In my life, I'd want to continue on with a therapist after starting T, but I've been through a lot, personally, in the past year or two. You should be able to say you're trans to any therapist and they'd understand. You might want to check your insurance though, some won't cover a GID diagnosis, if that's the case, convince the therapist to file under Adjustment Disorder or Evaluation code.
