It is important to recognise there was (and remains) no reference to the Sovereign as head of state in the Australian Constitution.

Indeed it appears our founding fathers deliberately chose to eschew the term and, through section 61 of the Constitution, assign the Governor-General powers that hitherto had not been given to any Governor or Governor-General anywhere else in the Commonwealth.

[Senator  Cory Bernardi, The Conservative Revolution, 2013, Connor Court,  Ballarat]