The questioner mistakenly believes there are no more handguns in Australia. And Hillary seems to think there are no legal issues involved in government efforts to restrict gun rights or institute forced buybacks; no mention of the Second Amendment and I suppose in her mind if she gets four years of picked Supreme Court justices, in effect we won't have a Second Amendment. Some sort of mandatory government buyback of weapons is, she said, "worth considering on the national level if that could be arranged."
Now, the actual situation vis a vis guns in Australia isn't as simple as the apparent media image of a nation where the government rose up in anger at gun violence and ensured that no guns exist and then everything got better because of that. (Here's a lot of the legal nitty-gritty.)
Australia is not a country without guns, by any means, and its vaunted gun homicide reductions were on pretty much the same downward trend before its beloved post-buyback new gun law regime in 1996.
But it seems to be true that personal defense is not considered a legitimate reason to be licensed in Australia, whereas the U.S. Supreme Court in Heller declared that self-defense in the home via common weapons is an inviolable constitutional right.
While it's hard to say what Hillary thought she meant by saying what she said, we see in the minds of her questioner and her fans that Australia has certainly come to mean "land where the government took all the guns."