The Queen’s representative in Australia appears to have backed the republican movement in a landmark speech.

Governor-General Quentin Bryce delivered the final Boyer Lecture of the year in Sydney on Friday evening, outlining her vision of a future Australia.

The ABC reports she expressed support for same-sex marriage, saying she hoped for Australia to become a nation where “people are free to love and marry whom they choose”.

Ms Bryce called for an Australia “where women’s contributions to civil society – the workplace, the economy, the family and home – are valued equally with men’s …

“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.”

The former governor of Queensland was appointed Australia’s first woman governor-general in 2008 by then-prime minister Kevin Rudd.

Governors-general serve at the Queen’s pleasure but five-year appointments are typical, meaning Ms Bryce is likely nearing the end of her time in the job.

The full lecture is due to be broadcast on the ABC on Sunday.

Same-sex marriage advocates were quick to praise Ms Bryce’s comments.

“The governor-general’s dignified support for marriage equality will be welcomed by the many millions of Australians who support the reform,” Australian Marriage Equality director Rodney Croome said in a statement.

“In particular, it will send a message to older Australians that this is a reform they can embrace because it strengthens relationships, families and marriage.”

Australian Republican Movement chair Geoff Gallop said it was time to restart the conversation about an Australian head of state.

“The governor-general has served with distinction as the Queen’s representative, but imagine what a powerful message it would send about this great country that we all love if we had a head of state who represented the Australian people,” Professor Gallop said in a statement released shortly after the speech.

“We will always be friends with Britain, but now we should be equals.

“We need an unambiguous, independent national identity that reflects and celebrates our freedom, our unity, our values of the fair go and our place in the world.”