I don't think they will. Regardless, the path to gun bans in the US would be markedly different than Australia's.
Have you not read the dissent in Heller?
"The majority’s conclusion is wrong for two independent reasons. The first reason is that set forth by Justice Stevens—namely, that the Second Amendment protects militia-related, not self-defense-related, interests. These two interests are sometimes intertwined. To assure 18th-century citizens that they could keep arms for militia purposes would necessarily have allowed them to keep arms that they could have used for self-defense as well. But self-defense alone, detached from any militia-related objective, is not the Amendment’s concern."
https://www.law.cornell.edu/supct/html/07-290.ZD1.htmlRead that again, and tell me that Justices Breyer and Ginsburg would change their opinion, or Justices Sotamayor, Kagan, and a new justice appointed by Hillary wouldn't agree with Souter and Stevens in this dissent.
To summarize: FOUR USSC Justices did NOT see an individual right to keep and bear arms. FOUR. IT WILL TAKE ONLY ONE MORE, and another Second amendment case, to reverse Heller.
It is either insufficient or disingenuous to just say "I don't think they will."