Dharma Trading Company sells packs of heavier freezer paper sheets. ( http://www.dharmatrading.com/html/eng/500944-AA.shtml )
They're more expensive than the grocery store but probably worth it. I just bought a new roll, so it'll be a while before i need to find out.
Bazillions of other places sell them, too. I mentioned Dharma specifically because I find their prices are usually lower than anywhere else and because you can get straight answers to your questions. The don't just sell products. They test them first and often ship extra instructions with them.
Their shipping services outstide the US are limited and expensive. The brand name is C. Jenkins Freezer Paper Sheets.
I googled it and found lots of sources. I'll bet you can find one in Australia.