Basically, no - you're not a citizen nor a permanent resident, so you're not legally eligible to own firearms in Australia.
So I will cower in my flat and hope that the police with keep the Muslim extremists in check. Not good for tourism. Yet tonight, I watch 7 news and they headline white extremists without mentioning the muslims caught with gasoline bombs on the Sydney bus to Bondi Beach on Sunday. The media here is far worse than in the U.S.