Baby Sussex has already received his or her first presents, thanks to Australia – with the beaming parents-to-be presented with baby ugg boots and a stuffed kangaroo with a joey in the pouch.

Governor General Sir Peter Cosgrove and his wife Lady Cosgrove presented Prince Harry and Meghan Markle with the gifts at Admiralty House in Sydney on Tuesday morning, after the royals met representatives of the 18 countries competing in the Invictus Games.

“Our first baby gift,” the duchess exclaimed on receiving the present – while an apparently delighted Prince Harry kept a firm grip on the tiny new boots.

It was the first engagement for the Duke and Duchess of Sussex on their first Australian tour.

Among the Invictus Games representatives were ambassador and former swimmer Ian Thorpe and his partner Ryan Channing, as well as Peter Leahy and Patrick Kidd.

The event was intended to focus on the Games, an event started by Prince Harry, 34, to help war veterans. He and Meghan Markle, 37, will open the games on Saturday.

But the real interest was in the news – announced by Kensington Palace on Monday night – that the royal couple are expecting their first baby next year.

For their first public appearance 15 hours later, Meghan wore an $1800 tight-fitting, sleeveless ivory dress by Australian designer Karen Gee. It revealed only the merest hint of a royal bump.

Ms Gee’s website reportedly crashed just after 9am, after Meghan stepped out in her Blessed design.

Keen royal-watchers spotted a tribute to the late Diana, Princess of Wales, in her daughter-in-law’s accessories.

#Meghan wearing Princess Diana’s gold and diamond butterfly earrings and bracelet on her first day of #RoyalTourAustralia pic.twitter.com/2InKbM8dHW

— Emily Andrews (@byEmilyAndrews) October 16, 2018

Harry, dressed in a navy blue suit, smiled proudly as the couple held hands on their tour through Admiralty House.

The sharpest-eyed among royal watchers had been expecting the baby news for some time, following the Duchess’ choice of fuller-flowing outfits at recent appearances.

Nonetheless, the announcement took many by surprise, including Sir Peter and Lady Cosgrove. Upon learning it, they swiftly dispatched a staff member to buy the toy kangaroo and boots.

Sir Peter also gave the Sussexes two Akubra hats that Australia had made as a wedding gift.

“The Morrisons have asked us to pass on a gift for your trip to Dubbo,” the Governor-General said, handing over the grey hats.

NSW Premier Gladys Berejiklian was the first government official to meet the couple on Tuesday morning.

“It’s my fault if the weather is bad,” she said, despite the sunshine.

The royals then headed for Taronga Zoo, where they met two koalas and their joeys named in their honour, and officially opened the Taronga Institute of Science and Learning.

Harry ditched the tie for the zoo visit, while Megan donned a beige trench coat.

After the zoo, there was a boat trip across the harbour to the Opera House, to watch a rehearsal by the Bangarra Dance Theatre – where hundreds of adoring fans were also waiting.

Among the crowd eagerly anticipating the royal walkabout on the forecourt was 98-year-old war widow Daphne Dunne, who also met Harry during his previous visits.

Mrs Dunne and the Prince chatted again on Tuesday. He introduced her to his wife – with the cameras zooming in on the trio as they spoke.

“Congratulations, I think that’s marvellous,” Mrs Dunne said to Meghan of her baby news. “It’s just what Harry needs.”

She kissed the Duke and Duchess and gave them cards and flowers.

Daphne Dunne with Prince Harry and Meghan Markle. Photo: Getty

Tuesday’s royal duties were to finish with a reception back at Admiralty House.

On Wednesday, Meghan and Harry head to Dubbo to visit the Royal Flying Doctor Service and meet local farmers hard hit by drought.

There will be a public picnic in a local park and a visit to a school for  young Aboriginal and Torres Strait Islanders. The couple will also play netball and football with the students.

On Thursday, they will be in Melbourne.

The Sussexes’ jam-packed tour schedule includes 76 engagements in 16 days, with visits to Fraser Island, as well as Fiji, Tonga and New Zealand.

-with AAP