[Legbreaker]

Short answer - Not very long at all.
Longer answer - there will be major shortages after only a few months as international trade dries up. Given a few years and the re-establishment of some trade, as well as internal adjustments to industrial production, and Australia could well be on a path to self sufficiency in most regards compared to the rest of the world. It's those middle few years (upwards of a decade) which will REALLY HURT.

I don't know too much as yet about the New Zealand position, but given it's lower population and generally less industrialised economy, my guess is that although they're likely able to feed the people, they're not going to be able to support any troops outside their immediate borders.

I'm currently reading through a number of Australian government and army reports from the 1990s detailing the problems for the military should military logistic support not be available during extended operations (they mean more than about 6-8 weeks) and formations of even just a single brigade in size. The forecast at the time was bleak to say the least. Budget cuts over preceding decades had left the logistic units a mere shell, barely able to meet peacetime requirements. Also didn't help that the Australian military has since federation in 1901 been very much focused on the combat arms (primarily infantry) with logistics left up to initially the British, and later the US.

In more modern times it was expected civilian workers and equipment would be utilised at both the Australian end right up to just behind the actual fighting. As I've mentioned previously in this thread, this didn't work very well especially during WWII due to industrial action and outright sabotage by unions. In East Timor, 1999, the expected facilities and workers in Dili simply didn't exist so logistics units throughout not just the army, but the entire ADF were stripped of personnel and equipment just to get the supply ships unloaded.

It's almost as if politicians and senior military officers had completely ignored the most basic rules of warfare for over a century!