Hi Sarah,
I am going through the Monash Health Gender Dysphoria Clinic here in Melbourne, which also has a letter requirement. I had to write up a brief (1-2 pages) autobiographical statement on how gender dysphoria has impacted my life, with reference to schooling, friends, family and occupation. I rang up to clarify how specific I needed to be, and was told I could include as much as I felt comfortable sharing. Basically all they wanted was a brief understanding of my background before the initial session with the psychiatrist. I just wrote the one page outlining how long I have been questioning my gender identity, how I felt about it, why I have decided to come out now and so forth.
There are a couple of Adelaide girls here on the forums, so I'd imagine they might be able to help you out here, as well.
Good luck!