Gender clinics are really not that much better than if you just know which doctors to go to. There's no gender clinic in Perth for anyone who is an adult, so we have to just know which doctors to go to.
First off is finding a GP, who will refer you to a psych. The psych needs to give you a letter for what you want to do (generally you'll want HRT, then later you'll want SRS).
Finding a GP can be hard, but usually you just need someone who will refer you to who you want. They don't need to understand necessarily, they just need to be okay with writing referrals.
Ask around for who is a psychologist or psychiatrist who has treated transgender people before. This is crucial, because a psych who isn't familiar with transgender people will just tell you to see someone else. This can be disheartening when you wait so long to see anyone.
When you find the right psych they will then go through a procedure to diagnose you with gender dysphoria. Once you have this diagnosis you can take it to your GP, get a referral to an endocrinologist (again, someone who has treated transgender people before) and book your appointment.
The endo will take blood for tests, but should eventually prescribe you your hormones.
For surgeries it's a similar process. I haven't gone for that yet, so I don't have advice.
I will say that there are ways around some steps. Informed consent model can mean you skip a psych or endo. This means that by acknowledging that you're an adult and can make your own choices, you elect to have surgery or take hormones and are fully responsible for any regrets in the future. This is pretty cool, but you'd need to find a GP who is comfortable with it. Most GPs have never seen a transgender person though.