It depends! Did you graduate from an Australia Uni? If not, it will probably be difficult. If you did, the answer is most likely yes! However, you will need to secure a PR visa or a work visa. This is generally not too difficult now, and most hospitals will assist you with sponsorship.
The process of residency in Australia is very different from that in the US and Canada. First, everyone most complete a one year internship to gain full medical registration, then the plan varies depending on what you want to do. If you tell me what you want to do I can give you a better idea.