Forgive me for any errors because I haven't gone through the process in Australia myself, but I spent several months in Australian medical school and did extensive research on the Australian system so I have a little bit of knowledge.
Australia has a different system from North America in that you do not enter residency directly after medical school through a match. In fact, it's not even called residency...the residency equivalent is called "specalist training".
To familarize yourself with the Australian system, please read the following:
Medical eduation in Australia (Wikipedia Entry)
Training of medical practitioners in Australia
Anyway, the barrier for you as a Canadian student graduating from an Australian medical school is
GETTING AN INTERN SPOT. Australian citizens are given first priority in getting the intern positions after medical school and if there's none left for you then you are out of luck. However, if you can get an intern spot, then after working as an intern for a year I believe you can be sponsored by the hospital or something for permanent residence.
After getting permanent residence status, you are now equivalent to an Australian citizen (aside from that 10 year moratorium thing which sucks) and so you can continue on as an RMO and then later pursue specialist training.