Thanks for your question.
The appointment of Ministers of State (such as Deputy Prime Minister and Minister for Infrastructure and Transport) is covered in Section 64 of the Australian Constitution which states that “The Governor-General may appoint officers to administer such departments of State of the Commonwealth as the Governor-General in Council may establish”. The 'Governor-General in Council' refers to the Governor-General acting on the advice of the Australian Government.
There are occasions when the Governor-General is overseas on official business, or on leave, and unavailable to act on the advice of the government. In such cases, a state governor is commissioned to act as Administrator of the Commonwealth and perform the functions of the Governor-General, including the swearing in of ministers.