Social media users also noted that Meghan was carrying two folders covering her stomach when she hopped off the plane in Sydney, suggesting that was more evidence of a pregnancy.
Prince Harry, the Duke of Sussex, and his wife will welcome their little boy or girl into the world next spring, and following the announcement on Monday morning Meghan's mum - who attended the couple's wedding in May without Meghan's father Thomas Markle - revealed her delight about becoming a grandmother.
The Duke and Duchess begin their tour in Sydney, Australia on October 16 and head to Fiji on October 23, Kensington Palace said.
Prince Harry and Meghan's child will be seventh in line to the British throne.
Britain's Prince Harry (L) and Meghan Markle (R) kiss as they exit St George's Chapel in Windsor Castle after their royal wedding ceremony, in Windsor, Britain, 19 May 2018.
The couple are now in Australia on their first overseas tour, which also includes New Zealand, Fiji and Tonga.
Speculation that the Duchess might have been pregnant grew on Friday at the wedding of Princess Eugenie.
Meghan Markle, Prince Harry expecting first baby
The 34-year-old prince, who married american actress Meghan Markle at Windsor in May.is now sixth on line to the throne. The news about Meghan's pregnancy was announced by the Kensington Palace on their Twitter handle.
"The Queen was told, the Duke of Edinburgh, the Prince of Wales, the Duke and Duchess of Cambridge, the Duchess of Cornwall - they chose that day to spread the happy news around and then recovered and relaxed, got on a plane, came over here and then put out the news for the rest of us". "Wishing them all the best", May tweeted.
After the announcement that Harry and Meghan are expecting a baby, Morrison tweeted: "What fantastic news!"
On Monday, 52.4 per cent of the 1,000 respondents to a poll conducted by the Australian Republican Movement, said they wanted Australia to become a republic - the favourite response of 58.6 per cent of responders between 25 and 34 years of age.
Royal photographer Chris Jackson told CNN in May that some of his favorite pictures of the prince were taken in Lesotho as Harry spent time with the children being supported by Sentebale.
While it is the first child for Prince Harry and Meghan, it will be the fourth grandchild for Prince Charles after Prince George, Princess Charlotte and Prince Louis - the children of Prince William and Catherine.
Meghan - an American former actress who starred in television series Suits - met the Prince through a mutual friend in 2016.
Congratulations have poured in for the couple from around the world.