Australia has exceptional demographics that make this possible - for the moment. It won't last, for the same reason it won't in Europe. But, you get to gloat for quite a while as an Australian, it'll last decades longer than in Europe, where unemployment makes the current situation untenable. To put it bluntly: Australia has a participation rate of 65%, dropping slowly (ie. pretty much perfectly stable for the past, frankly, almost the past century). Europe has a participation rate of 55%. Now you might think that's not a big difference, but it's the difference between 1 worker paying for 50% of a non-worker versus 1 worker paying for 80% of a non-worker. That means the life of close to 2 people needs to be financed from one job in the EU, whereas in Australia it's just slightly over 1.
Keep in mind that there is even more leverage, as people who are only employed to take care of the elderly, the young, ... make up a significant part of the workforce and shouldn't be counted as employed for this purpose (a geriatrician, a teacher, a nurse, ... is paid from taxes to take care of non-workers, that means he doesn't contribute to the economy). Therefore the numbers in Australia, are about 1 for 1 (ie. tax rate of just shy of ~50%), in Europe the numbers are really about 1 for 3 (ie. total tax rate of slightly over ~75%)
But even in Australia it's essentially over. Australians should have started to have way more kids about a decade ago to prevent what's now pretty much inevitable. Although once again Australia gets to sit back and watch what happens in other economies before it's forced to take action itself, like in the financial crisis. It should do well. Doesn't change the outcome though : taxes in Australia will have to rise to halve your post-tax income over the next 2-3 decades. In Europe ... let's not go there, taxing at 100% would not allow for enough economic activity to support the pensions and healthcare at the current level of provided care. Dedicating all economic activity in the EU to just that single purpose is ... not enough. Therefore, elderly care and health care will have to scale down, a LOT (and may God help them if Trump follows through on forcing Europe into defense spending). The basic problem is, the lower the working population gets the more massive the advances in productivity (the economic kind) have to be. There is a slight issue with that:
http://www.tradingeconomics.com/european-union/productivity
(I've had healthcare in both Europe and Australia though. Let me tell you, Europe is better. Though I guess it does greatly vary based on the exact location)