Definitely not insiginificant to its enemies- the ANZUS, and UKUSA treaties, if present in Fallouts world (which is likely given they're the result of the British Empire's limited ability to protect its Interest in the Pacific in WW2) would have drawn Australia, and potentially New Zealand, into the war on the American side.
Yet in fallout, it seems that pretty much all diplomacy is out the window, with USA annexing Canada, UN being disbanded, Europe being torn a new one via the resource wars, etc. So I highly doubt we would have joined with America, England or any other nation if nobody were "friends" anymore. Yet logically, if an enemy power decided to invade us or draw us into the war, they would have to: first, calculate the odds of success, determine what would be gained in the endeavor, and compare that to what such an undertaking would cost and then pitch that to their politicians (assuming that their country is not under military rule). In hindsight, an invasion/incursion with Australian forces would result in losses so heavy, it would demoralize any force with two brain cells, cause the entirety of Australian society (less women, children & elderly) (and assuming it was an invasion) to fight back with determination that would make japanese martyrs look docile and leave both their home country AND Australia easy pickings for a force with the will to seize opportunities when they see them (I'm looking at you USA -__-).
That aside.
While this is true, I believe that in the fallout world (and in our world), if they decided to nuke us, that the only places worth nuking are Melbourne and Sydney, being that they are the most heavily populated of Australia's main cities. There's also the point that both perth and the area's around brisbane are teaming with natural resources, while adelaide and darwin are not populated enough (in my opinion) to be worth an extra nuke. Now these points made, two nukes, while highly demoralizing, are not enough to entirely kill every person capable of surviving in a post apocalyptic scenario, even with radiation taken into account.
Another reason why Australia would survive is that we take care of our mates, are more than smart enough to create a vault system (possibly better than America's system that was designed by scientists working for sadist businessmen) and are resourceful enough to rebuild after the rest of the world goes the way of the dodo's.
Before anyone comments on why Australia have not invaded America, it is because that, largely, we honestly don't give a damn about America, we couldn't care less about it prewar, and we couldn't care less post-war. Thats just how we Aussies are, we are satisfied with the country we have.
Oh my, that turned into a rant rather quickly, if you bothered reading the whole thing :cookie: have a cookie :disguise: