He says the prerogative powers are exercised as the Queen's representative, and that is true. However, as the prerogative powers are common law, and common law is over-ridden by legislation and the Constitution supersedes all legislation except as expressly provided, the constitutional powers of the Governor-General are his own. These are the powers expressly defined in the Constitution, such as the power to appoint Ministers. They form part of the prerogative powers of the Queen in the UK, but as they are here defined by legislation, they are no longer prerogative but constitutional (or more broadly, statutory). 

 :::::::::A quote from McGarvie's book - the original is available online and is well-sourced - helps make the situation clear, though I urge all with an interest in this topic to read further before and after the quote:  
 :::::::::The legal powers exercised by an operative head of state need to be further classified here in order to counteract the confusions about them which often exist in minds informed by English texts which explain powers of a different nature. Discussion of the powers exercised by operative heads of state does not imply that heads of state are or should be powerful people. Quite the contrary. A core objective of a system with a nominal chief executive head of state is to ensure that it operates so as to confine the exercise of the powers (with one exception, the reserve authority) to implementation of the decisions of Ministers of the elected government. The smooth and constant success of the present system in achieving that has led many to overlook that it is the operative head of state who has the legal right to exercise the powers. It is an easy intellectual slide to assume that because a Minister decides and the power is exercised accordingly, it is the Minister who has the legal right and exercises the power. 

 :::::::::The powers can be divided into statutory and common law powers. In Australia most of the powers are statutory, created by the Constitution or an Act of Parliament. Thus the powers exercised by the Governor-General which underlie our system of government, such as summoning or dissolving Parliament, issuing writs for general elections, assenting to Bills passed by both Houses, and appointing or dismissing the Prime Minister and Ministers, are all statutory powers created by the Commonwealth Constitution.