Andrew:
As has been mentioned, many here have worked with therapists and have benefitted from the effort. However, the key is to find someone with experience in gender issues as this is not a focus for most therapists. As Sydney is a large metropolitan area, I assume there are LGBT resources in town. Here in the US, anyway, many LGBT centers offer mental health services and many of those either don’t charge or do a sliding fee scale.
This might be a starting point:
https://www.psychologytoday.com/au/counselling/nsw/city-of-sydney
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