The Duke and Duchess of Sussex arrive for a two-week visit that will also take them to Fiji, Tonga and New Zealand

The Duke and Duchess of Sussex have touched down in Sydney to become the latest set of royals to holiday in Australia, opening the Invictus Games and spending a week touring the nation’s famous sites.

The royal couple will do what royal couples and tourists alike are expected to do: climb the Sydney Harbour Bridge, ride a Melbourne tram, explore Fraser Island and visit Taronga zoo, where they are likely to be photographed with a koala.

The trip, the official part of which begins on Tuesday, is also a charm offensive.

Facebook Twitter Pinterest Clockwise from top: Sydney, Fraser Island, Melbourne and Dubbo. Composite: Reuters/AAP/Alamy/Rex

The duke and duchess will follow in the footsteps of Prince Harry’s parents, Charles and Diana, who travelled to Australia and New Zealand on their first overseas tour together. This trip is the duke and duchess’s second official overseas tour, they visited Ireland in July and the couple will also take in Fiji, Tonga and New Zealand.

The trip is not without controversy. A former top Fijian diplomat has said it is “not the right time” for the pair to come to Fiji, due to the coming national election. The diplomat said the Fijian government may “take full advantage” of being seen with the couple, giving them an edge over the opposition.

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But in Australia the visit looks like it will be met with enthusiasm, and New Zealand prime minister Jacinda Ardern has said the couple will receive “a very warm Kiwi welcome”.

The Australian state of New South Wales is expecting thousands of people to turn out to each of the public events, called “meet the people walks” on the royal itinerary, including an event at Victoria Park in the rural city of Dubbo, at which 25,000 people are expected.

While in Dubbo, the duke and duchess are scheduled to attend a community barbecue. But Dubbo mayor Ben Shields told the Guardian he hoped the couple would also get the chance to enjoy another classic Australian meal: the meat pie.

Will the visit be effective in crushing republican stirrings in Australia? When Prince William and the Duchess of Cambridge visited in 2014, Prince George was dubbed “the republican-slayer” on breakfast television, as polling at the time showed support for Australia becoming a republic was at its lowest point in 35 years.

Satyajeet Marar, 26, a spokesperson for the Australian Monarchist League, said the interest in the royal family that is piqued by visits like this one can only be good for the monarchist cause. “Ultimately it gets people interested and reminds them of why what we have functions so well.”

But, Michael Cooney, national director of the Australian Republic Movement, said things had changed, even since 2014.

Federal opposition leader Bill Shorten has promised a referendum on the question of whether Australia should become a republic in his first year in office, should Labor win the next election, scheduled for 2019.

A poll in February showed that 52% of Australians agreed that Australia should be a republic, with just 22% disagreeing. Cooney is unfazed about the impact of the visit by the duke and duchess. “Basically royal visits are good for the republic movement,” he said. “Royal news is republic news, it drives interest and discussion.

“Obviously in this case, Prince Harry’s got a really particular and terrific reason to be here, which is for the Invictus Games, which will obviously be a really inspiring occasion,” Cooney said.

“But if you think about this visit, it’s actually a picture of what life would look like if Australia were a republic. Someone like Prince Harry comes here for an event like the Invictus Games … and he comes as a very welcome guest, but not as our head of state. It’s a picture of the future.”