Australia can barely scrape together a single Division on anything less than about 12 months notice. Any more and reservists have to be called up and trained.
Australia also has it's own oil reserves. It may not be massively productive Fields like Texas or the North Sea, but there should be enough production post nuke to support the country's vital needs (especially if a couple of the cities got hit).
Regarding China vs Korea, Korea would get the troops without a doubt. Korea is essentially a UN operation (regardless of who's actually commanding), while China is basically a fight between two sovereign nations - the USSR (plus allies) and China (plus whoever was in the area and got caught up in it).
North Korea has long been seen as the BIG EVIL in the area, much more than the Soviets. North Korea also has no/less nukes (depending on how you want to look at it), which means less likelihood of Australians being irradiated.
Regardless of where the troops went, the moment hostilities broke out with Indonesia they would be recalled - Australia simply doesn't have the manpower to hold off such a huge military (even a poorly trained, led and equipped military as Indonesia at the time). Same thing happened in WWII when the Japanese were coming across Papua New Guinea - the Divisions in the middle east (mainly northern Africa) were recalled immediately and sent from the deserts to the mountainous jungles.
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