Governor-General Quentin Bryce has publicly backed both Australia becoming a republic and gay marriage in a landmark speech in Sydney.
Ms Bryce, delivering the final Boyer Lecture of the year, said she hoped Australia might become a nation where "people are free to love and marry whom they choose".
"And where perhaps, my friends, one day, one young girl or boy may even grow up to be our nation's first head of state," she said.
Ms Bryce was appointed as Australia's first female governor-general in 2008 by then prime minister Kevin Rudd.
While there is no set length for the appointment, most last around five years.
Ms Bryce used her address to call for a nation where "an ethic of care guides the way we lead".
"Where the young, the elderly, Indigenous, the newly-arrived [and] people with disabilities are treated with dignity and respect and are able to be the best and healthiest they can be."
The governor-general is appointed by the Queen on the advice of the prime minister.
Ms Bryce was born in Longreach, Queensland, and had a lengthy career in law before taking up the governor-general position in 2008.
She has been recognised as a trailblazer for women: one of Australia's first female barristers, she was later the first woman appointed to the University of Queensland's law school.
She has credited her mother, who was a teacher in Winton, with playing a big part in her early development.
"Growing up with notions of equality, of opportunity, they were always there for me," Ms Bryce told Kerry O'Brien in an interview in 2008.
Speaking about the republican debate, Ms Bryce said in 2008 that Australian society is "maturing and evolving" and that future debates about the head of state would be important.
"And I think we have a big responsibility to be very well informed about the evolution of the constitution."