The best term is: The Commonwealth of Australia is both a representative democracy and a constitutional monarchy with Queen Elisabeth II as Australia's head of state.
The Commonwealth of Australia was formed on January 1, 1901. The rules of the government were established in the Constitution. The Constitution created a federal system of government.
Representative democracy is a type of democracy where elected officials represent a group of people.
A constitutional monarchy is a form of government where a monarch acts as the head of state within the parameters of the country's constitution.