I would have to disagree with the first part. While Indonesia has higher PPP GDP than Australia, Australia has much higher absolute GDP. Remember, population size does not necessarily indicate GDP. For example, Germany's population is not that high, but only three nations beat it in nominal GDP (four if you use PPP).
Personally, I think Indonesia does have incentive and need to build a strong military. The same can not be said about Australia. Who are they gonna fight? New Zealand?
Australia has been more active in global conflicts and has a decent military history. I doubt they will go the route of Iceland.