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

The Duke and Duchess of Sussex held the first engagement of their first Australian tour at Admiralty House in Sydney on Tuesday morning.

The event was to focus on the upcoming Invictus Games, an event started by Prince Harry to help war veterans.

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

The Sydney sun shone on their first public appearance 15 hours after the news broke of her pregnancy.

Meghan wore a tight fitting, sleeveless cream dress by Australian designer Karen Gee that barely revealed a royal bump at all.

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

The announcement took many by surprise including Governor-General Sir Peter Cosgrove and Lady Cosgrove, who dispatched a staff member to hastily purchase a toy kangaroo with joey for their pregnant guest.

The visit coincides with the Invictus Games in Sydney, which kick off on Saturday and run for a week.

Prince Harry who served with the British Army for a decade, including included two tours of duty in Afghanistan, set up the Invictus Games after visiting the US Warrior Games in 2013, when he saw the positive impact sport was having on the recovery and rehabilitation of wounded servicemen and women.

The royal couple met with representatives of the 18 countries competing in the games at Admiralty House.

They then met invictus Games officials including ambassador and former swimmer Ian Thorpe and his partner Ryan Channing, as well as Peter Leahy and Patrick Kidd. 

They then posed for the standard shot with the Opera House in the background.

NSW Premier Gladys Berejiklian, was the first government official to meet the pair, after they greeted Invictus Games flag bearers.

“It’s my fault if the weather is bad,” she told the smiling couple in the sunshine.

After their meeting with the Invictus Games representatives, Sir Peter presented the couple with the baby gifts and the Akubra hats 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 two grey akubra hats.

They then headed for Taronga zoo where they'll also meet two joey koalas named in their honour, before heading to the Opera House to watch a rehearsal by the Bangarra Dance Theatre.

Afterwards, they'll do a walkabout on the Opera House forecourt to meet eager royal fans, including 98-year-old war widow Daphne Dunne who has met Harry during his previous visits.

Tuesday is the first opportunity for the public to interact with the couple - and to be the first to congratulate the royal couple.

In a jam-packed schedule of 76 engagements across 16 days, the royal duo will visit Sydney, Dubbo, Melbourne and Queensland's Fraser Island as well as Fiji, Tonga and New Zealand

AAP