@Jennie_Lou I had my surgery through Mater Public in Brisbane and Radiation there as well although I think technically radiation falls under the PAH. The appointment letters were very confusing :) They will triage you based on your initial referral and scans/pathology and schedule you in. I had a wait of about 10 business days for the initial appointment with the surgeon and a week later was in hospital. It happens pretty fast when it gets going. I was very pleased with the care I got as a public patient.
I did however switch to a private medical oncologist after active treatment. That's an important thing to know - you can mix and match public and private however you feel comfortable. You are not bound to stick with one option.