Departing royals leave crowds and controversy behind

King Charles and Queen Camilla have jetted off, ending a whirlwind Australian tour and prompting questions over when they might be back.

Monarchists hope for a return as soon as possible, while republicans want a local head of state to welcome future royals.

The visit made global headlines after an outburst by Independent Senator Lidia Thorpe who disrupted an event in Canberra, shouting at the King that she did not accept his sovereignty.

Australia is now back at the end of a long line of nations waiting to receive the recently crowned monarch.

University of Sydney associate professor of history Cindy McCreery said the King had been under pressure to prove himself and his health.

"On both counts, Charles managed to convince most, if not all people, that he is a sovereign who takes his role very seriously," Dr McCreery told AAP.

"The fact that we saw a diverse response to the King is quite in keeping with the diversity of Australia."

The King and Queen were farewelled on Wednesday by a small crowd, along with NSW Governor Margaret Beazley, Deputy Premier Prue Car, Home Affairs Minister Tony Burke and Governor-General Sam Mostyn.

The pair waved from a Royal Australian Air Force jet, later landing in Samoa for the Commonwealth Heads of Government Meeting.

Dr McCreery said the tour was built around that meeting, as was a previous visit from Queen Elizabeth.

The Australian visit was the first for a reigning king.

Australian Monarchist League royal tour spokesman Alexander Voltz told AAP the tour showed the King was committed to duty.

"There's not too many of us who would go halfway across the world, to do our job basically, with a cancer diagnosis," he said.

"We'd love him to come back. Of course, everything is contingent on his health but we wish his majesty a very long reign."

Australian Republic Movement co-chair Esther Anatolitis hopes it's the last time the nation's head of state visits.

"It doesn't make sense to have a part-time, foreign-based, non-citizen, above-the-law head of state who is not ultimately responsible or accountable only to us," she told AAP.

A future Australian head of state would still welcome royals as respected foreign dignitaries.

"Relationships evolve but friendship endures," Ms Anatolitis said, quoting Prince William.

The royals kept a packed itinerary, visiting Parliament House and the War Memorial in Canberra.

In Sydney, they were pushed to the brink, visiting the National Centre of Indigenous Excellence, a food bank, a social housing project, a literacy initiative, a community barbecue, a meeting with cancer researchers and a naval review.

The King and Queen greeted crowds at Sydney Opera House on Tuesday afternoon, where thousands queued hoping to meet them.

Others faced inconvenience, with scenic afternoon running routes disrupted, while one group of young women from Adelaide, visiting for US popstar Olivia Rodrigo, were surprised to see so many queuing to glimpse royalty in the flesh.

Plenty in line held Australian flags, about 15,000 of which Mr Voltz estimated the league's volunteers handed out.

Republicans sold conversation-starter shirts online, reframing the visit as the monarchy's "Farewell Oz Tour".

Prime Minister Anthony Albanese said the royals met a range of Australians who demonstrated the nation's best.

He looks forward to seeing the King in Samoa, where a Pacific nation will host commonwealth leaders for the first time.

The biennial meeting brings together 56 commonwealth countries, most of them republics, and is expected to discuss climate change, the impact of colonialism and reparations.

The latter topics featured during the tour, headlined by Senator Lidia Thorpe interrupting a reception in Canberra to declare King Charles was "not our king" and demanding the return of land and Aboriginal artefacts.

Monarchist campaigners will "explore" whether the senator breached an oath of allegiance, Mr Voltz said, adding the issues raised were for parliament, not the King.

Parliamentarians at all levels should instead swear allegiance to the Australian people who elect them, Ms Anatolitis said.

One thing they can agree on is that Australia's future is its own to decide.