As Bazz mentioned, the Port Arthur massacre was a big turning point in Australian's attitudes toward guns. This was around 15-20 years ago. There has been a lot of knee jerk reactions from law makers since. Unfortunately legal firearms owners seemed to have taken a lot of hits from these events in the form of harsher restrictions. Not saying they've all been unnecessary, but initially the laws often focused around ownership restrictions rather than punishments for doing wrong. But recently there have been a few harsher punishments imposed for those not abiding by existing laws, which is good to see.
There is currently (in S.A. at least - not sure about the rest of Oz) an amnesty in place until the end of August. Anyone who owns an unregistered firearm, or one without a serial number, can hand it to police without copping a fine or jail time. The idea being to reduce numbers of illegal guns in circulation. So this may be the gun grab you're hearing of at the moment.
Before you can get a firearms license, you need a police clearance. This involves a personal background check so they can rule out anyone with a violent history or tendency to ignore authorities. Guns don't kill people unless they're in the wrong hands.
I wasn't around in the good ole days, but have been told that once upon a time, a young Australian lad could take his gun to school or a friends property, and get a free bus ride there. The public opinion then was that he was capable of defending his country, and so deserved a free ride
Nowadays public opinion is heavily swayed by media. And in movies, only police and criminals have guns. So if you're not an officer of the law but own a gun, you must be a bad guy who wants to kill everything