Why is it that the Prime Minister and Cabinet are not mentioned in the Australian Constitution?

Great question!

You're quite right; the Prime Minister and Cabinet are not mentioned in the Australian Constitution. In fact, the Constitution does not cover all aspects of the governance of Australia. While central to the way the Australian Government works, the Prime Minister and Cabinet operate by convention – tradition –, similar to the British system from which they were derived.

Section 61 of the Constitution gives executive power to the King (represented by the Governor-General). This may suggest that the Governor-General has sweeping powers; however, in practice the Governor-General acts on the advice of the Prime Minister and ministers.

Section 64 requires ministers be members of Parliament. This gives us responsible government; ministers are elected representatives and are accountable to the Parliament. Section 62 describes the Federal Executive Council, which comprises all ministers past and present. Since Federation, the real Executive power has been held by the Prime Minister and the Cabinet, not the Federal Executive Council.