Northside and Prarhan Market Clinic will both refer to you have at least 1 session with a therapist, mostly to make sure any other issues are well managed. If you are looking for a surgical referral, either of these would be my option. You need to get a referral from an appropriately qualified psychologist or psychiatrist for that - there is no Informed Consent when it comes to surgical referrals.
As far as walking in to a random GP and walking out with a prescription? It probably happens, but you might have to try quite a few GP's before you find one that will. As I had already been on hormones for several years, I found that my local GP was happy to prescribe.