When the usual suspects start invoking 'Australia model',

they do NOT mean licenses and restrictions: they mean confiscation.
The crucial fact they omit is that the buyback program was mandatory. Australia’s vaunted gun buyback program was in fact a sweeping program of gun confiscation. Only the articles from USA Today and the Washington Post cited above contain the crucial information that the buyback was compulsory. The article by Smith-Spark, the latest entry in the genre, assuredly does not. It’s the most important detail about the main provision of Australia’s gun laws, and pundits ignore it. That’s like writing an article about how Obamacare works without once mentioning the individual mandate.
Because most of them don't have the guts to openly say what they actually want.

Yet when American gun control advocates and politicians praise Australia’s gun laws, that’s just what they’re doing. Charles Cooke of the National Review shredded the rhetorical conceit of bellowing “Australia!” last year after President Obama expressed his admiration for gun control à la Oz:

You simply cannot praise Australia’s gun-laws without praising the country’s mass confiscation program. That is Australia’s law. When the Left says that we should respond to shootings as Australia did, they don’t mean that we should institute background checks on private sales; they mean that they we should ban and confiscate guns. No amount of wooly words can change this. Again, one doesn’t bring up countries that have confiscated firearms as a shining example unless one wishes to push the conversation toward confiscation.

They do like invoking the magical words 'gun buyback'.  Two problems with that:
You can't 'buy back' something that never belonged to you,
and
Someone saying "Give us your property or we'll throw you in prison.  Protest too much and we'll kill you.  But we'll give you a little money, so you don't feel so bad about this" is still confiscation under threat of prison or death.  They just don't like to talk about that part.

Also, something said by the Australian Prime Minister, John Howard, while he was telling us we ought to do what they did:
Our challenges were different from America’s. Australia is an even more intensely urban society, with close to 60 percent of our people living in large cities. Our gun lobby isn’t as powerful or well-financed as the National Rifle Association in the United States. Australia, correctly in my view, does not have a Bill of Rights, so our legislatures have more say than America’s over many issues of individual rights, and our courts have less control. Also, we have no constitutional right to bear arms. (After all, the British granted us nationhood peacefully; the United States had to fight for it.)
He thinks it's better not to have a Bill of Rights, because that way the government can decide just what your rights are.

For the moment.  They're subject to change at any time this way.  And the courts can't get in the way so much.

Let me say this with great feeling to Mr. Howard and anyone else who thinks this way:
Screw you.  And screw your 'The .gov should decide what your rights are' bullshit.  We've got a bunch of politicians who wish they could rule that way; right now they're trying to do more damage to that troublesome 'due process' thing that gets in their way; they're being told, with loud voices, just what they can do with that attitude.

Oh, they don't care; after all, they know better than we what's good for us, so our opinions don't matter.  Neither does their oath to uphold the Constitution, which tells you exactly what their word is worth.

They do know(the honest and non-stupid ones, at least) that the real reason they can't get their crap through is because so many people tell their congresscritter "Vote for this, and your ass is out at the next election", and the critters know they mean it.  And the bigots and hoplophobes can't stand it.  They also don't want to acknowledge that, so we hear all the crap about the 'evil NRA that wants people to DIE!!', and Fauxcahontas screaming "The Republicans want to arm ISIS!!"

Screw 'em all.  And make sure your congresscritter knows just what you think, and that you damn well mean it.  As Lawdog said, they've already stolen most of our cake, and we're working on taking it back, a piece at a time.