How come Australia hasn't had the same social and political crises (such as assassinations and coups d'etat) that characterize other nations with arguably similar traditions and cultural mixes?

We've had a few rebellions, but nothing to the scale of a national revolution. They've included notably the Rum Rebellion (1808) -- a military coup that got rid of a governor, which was also about the only time that an armed uprising has ever succeeded in overthrowing and replacing a government in Australia -- the Darwin Rebellion (1918), and of course the 1854 Eureka Rebellion (which ended in bloodshed and trials, but the short-term failure helped gain suffrage later on). There were certainly many other 'crises', just on a different scale, whether brawls on the Victorian goldfields between groups, some of which included different ethnicities (e.g. Chinese immigrants), or particularly savage frontier wars against Indigenous tribes. One structural reason is that, in the earlier days, these were convict settlements, with a strong military presence and an incentive-based labour system, and which moreover constituted settler and not exploitative colonialism, so investments did flow into the various colonies and so forth. I'm sure others can provide much more substantial responses to answer your question -- I say these few points as simply some preliminary ideas and to help discard the view of Australian history's reputed 'dullness' when it comes to uprisings, more than anything else.