The application process to each Australian medical school is different and therefore you must look up at each of their website to gain more knowledge. Some of the undergraduate schools use a common moderating examination UMAT (Undergraduate Medical and Health Sciences Admissions Test) while entry to the graduate programs requires successful completion of GAMSAT (Graduate Australian Medical School Admission Test).
You have to enrol in the undergraduate medical programme in a college that offers a Bachelor of Surgery/Bachelor of Medicine (3-4 years). Then follow it up with a postgraduate medical programme that will take 2-3 years.
You will need to pass the Graduate Australian Medical School Admissions Test (GAMSAT) to be admitted to such a programme. After earning both the medical degrees, proceed with starting your residency as an intern for 1 year then as a resident for another year.
During this year you can decide on the specialty you want to choose. After completing your residency you should begin with your specialist training programme which can take 3-6 years (theory+hospital training). After that you would need to clear an exam to start working as a specialist.