And I don't think they have right to carry in Australia. So its effectively a ban on gun ownership even if that's not de jure.
Under Australian law, if you believe you, or another person, is in danger of death or serious injury, you can do anything and use anything to defend yourself - including a gun. We do have a right to self defence guaranteed in common law and that is what it says. It's true that most people cannot get a licence issued simply by saying they want a handgun for self defence - that by itself is not sufficient reason - but if you have one issued for another reason, you can certainly use it in that way. The simplest reason for most people is to be a member of a gun club.
And I don't think they have right to carry in Australia. So its effectively a ban on gun ownership even if that's not de jure.
The 'right to carry' is a peculiar provision of American law and doesn't have any analogue in Australia because it doesn't really have any relevance in Australia - that is, we haven't had the same legal history you've had, laws and court decisions here have gone differently. If a person is licenced to own a firearm, simply by virtue of that fact, they can take that firearm into most places unless the place is expressly excluded or their licence is specifically restricted. It's never needed to be stated in terms of a right to carry, any more than you need a 'right to drive' on public or private roads, if you have a driver's licence. It's part and parcel of the licence. Some people do have more restricted licences. Plenty of people don't - though it does take some effort to get such a licence. Long arms are actually more complicated because there are legal precedents that make carrying an obvious weapon around a 'breach of the peace' in quite a few cases.
I don't carry a handgun often, but when I do, there's very few places I can't carry it (Courts, and certain other government buildings, mostly).