I would be surprised if they're burning much fossil fuel for heating, most Australian homes use electric heating of some form. We don't really have basements, so no boilers, and gas heaters were phased out a decade ago.
But more than the technical achievements, it's a political achievement too. Australia has been mired by coal mining influencing policy for decades, and in the past ten years states have been reacquainted with their fortitude and started making policy that helps the state and not the mining industry.
SA and Tasmania are full steam ahead on renewables and they are leading by example on just how capable new energy technologies can be when deployed with smart policy.