Hi Nattie,
I am in Melbourne and have been on HRT for almost 6 months. My thoughts somewhat thrown together follow!
Find a GP that is experienced with LGBTI patients. It is a bit faster and a referral can get printed while you are still saying "Hi". The 2 that specialise are Prahran Central and Northside. I go to Northside. When I rang for an appointment, I explicitly said I wanted a GP to write a referral to a psych and what for. I understand that there may be a wait at Northside for new patients. If so, either wait or go to Prahran. Try your own GP too. Mine pretty much declined due to lack of experience. A referral does mean Medicare contributes. The psychiatrists seem to require one.
Psychs - I only have experience with Fintan Harte. Only a 5-week wait and spent 7 sessions with him but the 7th was us writing and reading his report. I am in my 50s too with marriage, family and career so he was probably being cautious. In the end, he came up with a diagnosis but I feel like it was "extremely well informed" consent. I am seeing him for a follow-up this Friday - he wants to stay in touch and continue to help if he can. If you go to the Joy FM website, you may find some podcasts of Fintan talking about his approach. The other specialist psych is Jaco Erasmus in Moonee Ponds. Haven't met him.
Fintan also referred me to La Trobe Uni for voice work so the specialists are useful. I also see a psychologist just for counselling. She too specialises in this stuff.
My GP prescribes and does all my HRT stuff. I love him. Spends most of our time together talking about how I am going and how my family is (they don't go there). It helps he (he says "we") hit the E ad T levels we wanted straight away. I see him again next week so we will see where things are at.
I am sure there are other providers in Melbourne. As Cindy said, ANZPATH is a very good place to start. Those I have dealt with are all really nice to deal with and I feel very well looked after.
Let us know if you have any other questions.