Semi-automatic rifles, especially centerfire, and especially those that look even vaguely military, are a pain in the ass to get a license for. Same goes for pump & semi-automatic shotguns, which is why pump-action rifles and lever-action shotguns have gained some popularity there.
It's not just a pain - it's basically impossible in every jurisdiction.
You need to prove some sort of need/reason to own a gun here. If you have ranch property and permits for animal control, or hunting, that might do it. Joining a shooting club and shooting a certain number of matches each year is another way to do it. You need permission for every purchase, a licence to possess, and to meet safe storage and handling requirements.
But it is most definitely do-able.
Kangaroos are overpopulated too. Rabbits scrub the earth clean, starving sheep and native fauna.