No.
They'd need to get a Category H handgun licence, and that doesn't happen overnight.
How long it takes depends on which state you're in. In my state, getting a H licence from scratch tends to take between six weeks and three months, provided you haven't got a criminal record. It's supposed to take less than four weeks, but in my experience, it's normally more like six to twelve. You're also going to find it a lot easier to get one, if you join a pistol club.
In my state, which has some of the stricter rules in Australia, you also need to get a 'permit to acquire' any new firearm. Last time I did that, I got the permit in three days, but that can also easily take up to four weeks.
It's a bureaucracy. It's not good.
But it's not that hard to navigate it.
These are the Glock 17s available for purchase at my local gunshop.
They have a pretty limited range but the Glock 17 is something they do carry.
It isn't particular concealable, because we do have laws concerning minimum barrel length for handguns that basically make easily concealable handguns much harder to own, that means the ordinary person probably get a licence for one of those.
Most people are also very limited in your ability to carry a firearm on a regular basis. I'm actually less limited than most in that regard, but my situation is unusual (I'm a retired Naval officer, and - well, there's other reasons as well, that means I'm not entirely typical. But it's not that hard for any lawabiding adult to own a handgun, even if they don't all have the same latitude some of us do).
We have plenty of dumb gun laws here.
But we're a hell of a long way from disarmed.
If we were, I would hardly have a local gunshop to link to.
Most people are also very limited in their ability to carry a firearm on a regular basis. It is generally assumed you will have it locked in a safe somewhere, unless you have a very specific reason to be carrying, and personal self defence is not, by itself, considered sufficient. That obviously does have real limitations on the utility of owning a handgun whether that is legal or not.