To seek HRT, either of these two medical clinics is a start. They use the services of the same psychiatrists, so which ever clinic you would like.
Prahran Market Clinic
It disappoints me that you can't ask your parents for help and even more so stating that a reason is because they are "Christian". Well I am a Christian and I am transgender female.
I think some Christians are so far away from Jesus in their every day lives that they are better served describing themselves as "lost" rather than "Christian".
God created you, I, and all things. Being transgender is neither good nor bad ... it is a natural created state. How we live is what matters. Being transgender or homosexual (which I am too as I am attracted to females) is normal ... not the norm, but life has a breadth of diversity and beauty beyond the societal puritan of straight female and male.
I just wanted to address this faith side of things, as I don't feel comfortable with persons professing faith, but lacking compassion and love. They do themselves and God a disservice.
Anyway, I hope this assists.
As for the cost, a Government issued concession card is accepted at either clinic. The psychiatrists, there are two, with the one north of the city no longer accepting Government concession cards. I don't know about the other.
I have completed voice feminization therapy and am four months into facial hair removal, and living full time as a female since the start of this year. I looked at HRT earlier this year and hope to revisit that again next year. For me, I feel I can do a lot myself, as the HRT requires seeking the approval of others.