Good question, Finn! Before Australia was a nation, it was a collection of British colonies. Each had its own written constitution, parliament and laws. When these colonies joined together to form Australia, a constitutional monarchy system of government was chosen for the new country - very similar to those of the colonies. More information about Australia’s Constitution can be found here and here.
Australia, like Britain, is a constitutional monarchy. The Queen is Australia’s head of state and acts in accordance with Australia’s Constitution. In Australia, the powers of the Queen have been delegated to her representative, the Governor-General.
As well as being a constitutional monarchy, Australia is also a representative democracy. This means that the people vote for delegates to represent their interests in a parliament. In Australia, members of parliament are elected to the Senate or the House of Representatives to represent the Australian people and make laws on their behalf.