In 1933 Western Australia held a referendum and voted 2 to 1 to secede from the rest of Australia.
In 1934 they sent a delegation to Britain to request that this be put into law, but the British faffed about and concluded that they wouldn't do it without the approval of the rest of Australia. The matter was put on the back burner, then World War 2 started and it was knocked off the stove entirely.
At the time 'The West Australian' newspaper printed a special edition of the case for secession. Here is part 1 of it in PDF format (16 mb)
Western Australia - Secession - 'The Case' for London - 1934.pdf
More information from The State Library of Western Australia
More information from the State Records Office of Western Australia