If the Prime Minister advises the Governor-General to do something, can the Governor-General refuse as they only act on ministerial advice?
Thanks for your question Lee.
According to the Australian Constitution the Governor-General performs the ceremonial functions of head of state on behalf of the King. While Executive Government powers are exercised by the Governor-General or in his or her name, such actions are carried out as advised by the Prime Minister and Ministers.
In some matters the Constitution gives the Governor-General the power to act independently, such as the power to dissolve the House of Representatives. However, in other than exceptional circumstances, the Governor-General will follow the advice of a Prime Minister who has the support of the majority of the members of the House of Representatives.
The powers that the Governor-General has to act without advice are referred to as ‘prerogative’ or ‘reserve’ powers and are not clearly defined in the Constitution. Constitutional experts do not agree on their precise extent or on the nature of the exceptional circumstances in which they may be exercised.
The Governor-General engaging in ceremonial duties.

Office of the Governor-General
Description
The Governor-General, wearing a suit and medals on the left side of his chest, talks to people in a crowd.