Yeah it's actually pretty hard to fire someone these days in Australia. It's been a long time since I read up on it and my memory is pretty hazy as I just haven't needed to (and I won't look it up now because I'm cooking dinner) but you need pretty valid reasons, and usually employers implement a "three strikes and you're out" system, with the first being a verbal warning, the second a written and the third is termination of employment. And the reasons have to be things like misconduct, defamation, illegal activities, turning up under the influence of drugs/alcohol, being late many times, etc. All pretty obvious really, but they can't fire you for things like they don't like your haircut or if you have a beard, unless it is strictly stated within their guidelines. Even then with something like beards (it was an issue for me with one manager at a previous job) they can't make an issue if it is well groomed (mine always is) and if a beard is grown it must be done whilst on leave.
tl;dr employers need to have valid reasons for termination that are preceded by verbal and written warnings. Gross misconduct, fraud and illegal activity can of course result in immediate termination of employment.