Hi, thanks for your question.
The Australian Constitution is the set of rules by which Australia is run. It describes the composition, role and powers of the federal Parliament. It sets out how the federal and state parliaments share the power to make laws, and details the role of the executive government and the High Court. However, you are right when you note that not every feature of Australia’s system of government is included in the Constitution.
The Prime Minister and the Cabinet are not mentioned in the Constitution. While central to the way government works, the Prime Minister and Cabinet operate by custom and convention, similar to the British system from which they were derived. There is also nothing in the Constitution about other party positions, such as leaders, deputy leaders or party whips.
The Constitution does not specify that the Government is the the party (or coalition of parties) with the support of the majority of members elected to the House of Representatives. However this has evolved as a necessary practice for the governance of Australia, which also has its origins in British customs and conventions.
The Constitution does not cover roles and responsibilities of local government. Local governments in Australia were formed by the state governments.