Yes, handgun and long guns are available in Australia but only to licensed shooters. Handguns and a handgun licence, is more difficult to get. You need to have a genuine reason to have a handgun; mostly its participation in Target Shooting. (There are other categories like Collecting and Security). Self defence is NOT a genuine reason to own a gun.
In my State of New South Wales, you have to first become a member of a registered Pistol Club. Once a member, you have to undertake some safety training and can then apply for a Probationary Pistol Licence. After 6 months, and after undertake three supervised shoots, you can then apply for a full handgun licence.
To maintain your licence, you need to shoot at least 6 club matches per year. You also need to remain a member of a Pistol Club.
Every time you wish to purchase a gun, you need to submit a Permit to Acquire to the Firearms Registry. Once you have this permit, you are then able to buy 1 x firearm within the 3 months allocation of it. You are submit multiple PTA's to FAR if you wish to buy a number of guns at the one time. Every PTA cost you $30 processing fee.
There are Safe Storage requirements and a Police Officer is required to attend your house and conduct a safe inspection. These Safe Storage requirements vary depending on the type of guns you have.