As an Australian who got taught Australian colonial history nearly every year at school (they were wonderful at varying it up), I think there were a couple of reasons (this is mostly what I know from school and living here, so bear with me, I could be wrong. This is also my first post on the site, so...). Firstly, Australia was being sent convicts up until 1840, about 52 years after the first British fleet arrived in Sydney Cove. Meanwhile, America had English colonies as early as 1610, and the Americans declared independence about 166 years later. If Australia had waited the same period of time, independence would have been declared around 1954, which was half a century AFTER we federated.
Australia had a very high population of 'lower-class' citizens in the 19th century, with a majority of people either being convicts themselves, or the children and grandchildren of convicts. Education was hardly widespread, and the development of an 'Australian' upper class was not quite in place. Many of the people in power were British, born in Britain and residing here. Until the 1820s, Australia was only a penal colony, meaning that the white population was either convict, former convict, or the marines and their families. Free settlers were not common at all.
English law was attempted to be installed into the courts, with the leaders of each colony (eventually states) being representatives of Britain, but being on the opposite side of the world to the English meant that things could be dealt with in harsher or less severe ways and easily remain unknown to the British - a lot of things were up to the discretion of the people physically in charge instead of taking every issue back to the book or to the English for a decision to be made. Initially the councils to govern the colonies were small and chosen entirely by higher-up people in Britain, but slowly they became representative governments, meaning that the (adult,white, male) people could vote on who would govern them to an extent.
There was an influx of non-British people living in the country, too; obviously, the Aboriginal peoples, but also many Irish and Chinese, particularly in the 1840s and 1850s as the gold rushes across the country boomed. One place in Ballarat (a big mining city in Victoria, a few hours from Melbourne) became home to an small uprising, the Eureka Stockade - sparked by two things, the death of a fellow miner whose killer was a publican and therefore let off, and the increase of cost on the licenses to mine and the brutality in enforcing those laws. It is interesting to note that the miners had a great deal of the average Victorian's support, and if they had triumphed against the British soldiers, perhaps it could've kickstarted a revolution similar to that of America. It began with a group of men meeting and deciding that they wanted votes for all men, and the abolition of the mining license's existence. Approximately two and a half weeks later, an even larger group of men came together and publicly burnt their licenses under a Southern Cross flag, which is often proposed today as being Australia's true flag if we were to become a republic, and is in fact displayed by many people around the country who would consider themselves in favour of Australia breaking away from Britain. These men then built a Stockade and stayed inside there, with some of their wives and children joining them. The battle was on the Sunday of that week, which took all of the diggers by surprise. They were severely outnumbered, had little fighting skill and were not expecting an attack, meaning that they were defeated in just twenty minutes. The legacy of this cannot be overstated; at the time it lead to an inquiry and later reform of certain laws about mining and voting, and it is interesting to note that later, Peter Lalor, who was the 'leader' of the Eureka Stockade, became the first Member of the Legislative Council in Ballarat. In our time, the flag sewn by three women on the minefields has come to represent which side of the debate you fall on, and the idea of the Eureka Stockade is heavily imprinted onto the mind of (most) Australians.
It is possible if action had not taken place, or if the miners had not been defeated, there could have been a bigger movement, and even a proper rebellion against Britain. I would say that Australia did not have as harsh conditions as the U.S.A, did not have as large a population in favour of breaking away as America did, and ultimately was around for a much shorter time than the U.S.A was.
I hope some of this helped and wasn't just incoherent ramble
