In the early years of the Australian nation (which was federated in 1901), not all states were pleased to stay as part of new young nation, such as Western Australia, who has over the years attempted to secede many times.
The year before Australia became federated, all states voted in referendum's to join the Federation of Australia, Western Australia was quite wary of this at the time as the had only just become self governing and didn’t want to hand the power back at a national level.
Western Australia's referendum was the last of the state's to occur, and got over the line, predominantly due to many from the eastern states working the goldfields in Western Australia at the time. Given the hesitation and lateness of their Western Australia, Western Australia was unable to be specifically mentioned in the Australian Constitution as there was not enough time to redraft it.
The first idea of seceding was raised as early as 1902, but it didn’t eventuate into much. Many Western Australia's felt the constitution was heavily favoured towards the eastern state's industries. By the early 1930's, the Great Depression had rolled around and was crippling the state, with its industry (mainly mining and wheat) suffering and unemployment rising. The Western Australia government felt that they were keeping Australia afloat with its industry without getting anything in return.
At this time the idea of seceding from Australia was growing in momentum, and was the topic of conversation in Western Australia. Many rally's were held at the time by pro-secessionist groups, however there was also anti-secessionist rallies being held at the time. In the early part of 1933, current Australian Prime Minister Joseph Lyons, and former Prime Minister Billy Hughes, went to Perth to support the anti-secession movement. The rally's weren't always peaceful affairs, and at one such event the Prime Minister was jeered by the crowd, with the crowd pelting coins at them, one hitting the Prime Minister's wife in the head.
In April 1933, the Western Australian government held a referendum to secede from Australia, which was further supported by the incumbent Nationalist government, but heavily opposed by the Labour opposition. Unfortunately for the Nationalists, the referendum coincided with the State elections. The referendum was a wild success, with 68% of the vote, voting for secession, but the Nationalist government was thrown out of office at the election.
Even though the new government was opposed to secession, given the overwhelming majority of the referendum vote, they went to London to request that the British government overturn the creation of Australian Federation and allow Western Australia to secede, with the Australians claiming that the Australian constitution had been created in the detriment of the west and in favour of the east.
The British House of Commons debated the matter for over 18 months before ruling that it could not legally do so, so the Australians went home.
After their failure in London, the pro-secessionist movement withered away, and by the time World War 2 came around, it was almost non-existent, although over the decades the notion continues to rear its head, and causes debate to this day.
Interestingly enough, the referendum results were never annulled, and still stand to this day.