You're quite right – the Prime Minister and the 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 custom and convention, similar to the British system from which they were derived.
Within the Constitution and through custom and convention, emphasis is placed on the role of the executive government, or the Prime Minister and Cabinet.
In the Constitution, section 61 says that executive power of the Commonwealth is vested in the Queen and is exercisable 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 executive. Section 64 of the Constitution refers to the appointment of ministers and requires that they be members of Parliament. This section underlines the principle of responsible government – ministers are elected representatives and are accountable to the Parliament. Finally, section 62 of the Constitution describes the Federal Executive Council, which comprises all ministers past and present. Since federation, the real power of the executive has been held by the circle of senior ministers, including the Prime Minister and the Cabinet – not the Federal Executive Council.
Although the Prime Minister and Cabinet are not directly mentioned in the Constitution, their respective roles have grown in stature since federation. Established practice dictates that the Prime Minister is a member of the House of Representatives.