I registered to say this.
I've been seeing Dr Linda Midalia. I can't express how much I've enjoyed sessions with her, so I really recommend her. She's been dealing with LGBT* issues and trans stuff for over 20 years and it shows in how she's managed to handle me.
Her site is here
http://www.lindamidaliapsychology.com.au/All of her contact info is on there. Unfortunately she does not bulk bill so there is a cost associated with seeing her and you will want to get a GP Mental Health Plan so that the first 10 visits per year can be processed with Medicare and you can be given about an $85 rebate.
She will likely want to refer you to the Northside Clinic in Fitzroy to see a GP. This is because there is a doctor there who will accept a psychiatric evaluation from a psychologist as a basis for HRT as opposed to the others you might find in the Prahran Market Clinic who would need an evaluation from a psychiatrist as well, which means more costs and more waiting for you.
I hope this helps.