They also got to meet the koalas in the sanctuary at Tidbinbilla, now thriving 20 years on from the firestorm which killed all of the koala population except for one - who was named Lucky.

The royal couple started their three-day tour of Australia in Canberra, their visit continuing on Tuesday at the arboretum, Australian National University and Parliament House, before they head to Sydney.

It is the first visit to Canberra for Crown Princess Victoria, who is the heir to the Swedish throne.

At the National Museum, Princess Victoria, 45, accepted flowers from Bonnie Heap, two, of Ngunnawal, amidst the scrum of local media as well as three photographers and three journalists from Sweden.

"We couldn't resist coming to see a real princess," Bonnie's mum Elyse said.

The visit to the museum included a smoking ceremony and Welcome to Country conducted by Paul House and a tour of the museum's Great Southern Land environmental gallery, which explores First Nations' connection to the continent over more than 65,000 years.

The royal couple met the museum's Indigenous Reference Group including chair and council member Fiona Jose and other Indigenous leaders such as Professor Peter Yu.

Princess Victoria chatted with interest about the artefacts and displays, but also showed a more laidback style, joking as the smoke from the smoking ceremony drifted away from her ("Yeah, yeah that's a good direction") and, when confronted with a model of a large crocodile, zipped quickly across the room ("I think I'll go over here").

The royals headed out to Tidbinbilla for the afternoon on Monday to meet emergency services personnel and visit the koala sanctuary. They rode to the nature reserve in a Volvo electric bus, their tour of Australia about promoting sustainability as much as relations between the two countries.

At Tidbinbilla, Princess Victoria spoke to ACT Rural Fire Service chief officer Rohan Scott about the impact of the 2003 Canberra firestorm on the nature reserve and the adjacent Namadgi National Park and the area's recovery over two decades. She said the landscape was beautiful - and vast compared to home.

"It's so difficult to grasp the size of everything here. It's just enormous," she said.

The royal couple were also presented with a book - Ablaze. The long, hot summer of 2019-20 - which was compiled by members of the ACT Volunteer Brigades Association.

The Crown Princess was stunned to hear the fire fight that spring and summer lasted six months, across many different blazes, up and down the eastern seaboard. Both she and her husband were moved by images in the book, taken by volunteer firefighters attending those fires.

They also spoke with Tidbinbilla Rural Fire Service volunteers Ross Turton and Sue Sayer and then sat with everyone else at the tables next to the Tidbinbilla playground, eating a lunch of sandwiches and maybe a sneaky Monte Carlo biscuit or two. And the princess hopped in a fire truck, her husband taking a photo for their two children back home.

Johan Forssell, the Swedish Minister for International Development Cooperation and Foreign Trade, is accompanying the royal couple.

He and the royals will meet with Australian ministers at Parliament House on Tuesday, with subjects likely to be covered including electrification, mining, healthcare and innovation.

On Tuesday, the royal couple will also plant a tree at the arboretum and Princess Victoria will speak at a seminar about electrification at the Australian National University.