Go to med school and become a doctor. Then do your intern year (PGY1). Then a year as a resident (PGY2). Then you are eligible to begin applying to most specialty training programs, which are through the various medical colleges (e.g. Royal Australian and New Zealand College of Psychiatrists, Australasian College of Dermatologists, Australasian College for Emergency Medicine, etc.) These each have their own requirements for entry to their training programs. It is competitive for most, some definitely more than others (surgery and derm being two examples), and by the time you get to the stage where you will be applying, it is going to be much, much more competitive than it currently is.
A lot of applicants who are successful have completed postgraduate masters degrees and PhDs, or at least published a lot of research. And a lot of applicants have to reapply multiple years in a row, while improving their CVs, before they are accepted. Training programs are between 3-7 years I believe, depending on the specialty, so the shortest timeframe you are looking at to become an accredited specialist doctor is 5yrs undergrad medical degree + 2PGY + 3yrs training = 10yrs. The reality is it takes most doctors much longer.