The firearms licensing laws vary from state to state, but as a general rule you need a 'legitimate' reason to own a firearm, and self-defence is generally not one of them.

For instance in NSW (the state that Sydney is in) - the NSW Police have a list of Genuine Reasons to own a firearm[1].

There's also other criteria you need to meet.

It means that day to day, as a general rule the only people you might encounter with a firearm are police officers. That is, unless you work in a rural area or in one of those related industries.

[1] https://portal.police.nsw.gov.au/s/article/Firearms-Licensin...

It's impossible to get a handgun licence for self-defence unless you work for a security company like Armaguard, who are only allowed to use guns for defence of property rather than bodyguard-style services.

and sport shooting yes