With a history of less than 250 years, European Australia is a young nation. Like the western regions of Canada and the USA, it has recent roots in frontier society, with characteristics such as economic inequality and a culture of machismo. Most of the continent is the arid Outback, their equivalent of Canada's frozen north. Like America's First Nations, Australia's Aborigines were largely overwhelmed by a combination of technology and racism.
The continent's first white settlement was a 1788 British penal colony, whose legacy can be seen in the egalitarian populism of today's society. (Those who hire Australian taxis sit in the front seat!) Indeed, Van Diemen's Land renamed itself Tasmania to distance itself from the notorious penal colonies of the past. The key event of the 19th century was the Victoria gold rush (around the same time as its California counterpart), ushering in prosperity along with wheat and beef exports. In 1901 half a dozen British colonies formed a single dominion through Federation, similar to Canada's Confederation.
Like Canada, Australia has a bit of an identity crisis. For a long time Australians saw themselves as a proud British society on the other side of the world, but large numbers of non-British immigrants have gradually fostered 21st-century diversity. Trade, once focused on the homeland, is increasingly turning to the growing economies of Asia. The popular self-image of open spaces and independent farmers notwithstanding, over half the population lives in five metropolitan areas.
For background reading, we can try Kenneth Morgan's AUSTRALIA: A VERY SHORT INTRODUCTION.