Australia uses British English for their spelling, which spells labour as in physical work, with a "u", where the Australian Labor Party spells it without a "u".This is in contrast to the British Labour Party which uses a "u".
Why the difference?
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The Australian Labor Party uses this spelling because, in 1912, an American-born Australian politician King O'Malley made a successful case to have the spelling 'modernised' to the way that the Americans spelt it. Some other Australian politicians just wanted to have the name distinguish from the worldwide labour movement, hence the change.