The youngster, who was sporting green glasses and a checkered cap with his school uniform, then handed the Duchess of Sussex a bouquet of flowers, before throwing his arms around her as well.
Speaking to Sky News afterwards, Daphne said Meghan was "really beautiful" and said she was delighted to have built up such a special friendship with Prince Harry over the years.
Her name is Daphne Dunne, and the 98-year-old has actually met Prince Harry twice before.
Samantha Markle said she was "very happy" with the news her half-sister was expecting her first child.
The Duke and Duchess have been busy in Australia keeping a full itinerary of appearances, collecting stuffed animals and meeting real ones at the Taronga Zoo.
"You are the salt of the earth, honest, hardworking and as tough as they come", he said.
The Royal couple are set to visit the Royal Flying Doctor Service first, where they will unveil a new plane.
The designer reportedly sent one of the "Royal Duchess" hoddies to Kensington Palace for the duchess to wear but the outing in Australia on Tuesday is the first time Meghan has worn one of Williams' designs in public.
Later on Wednesday, Harry and Meghan are expected to meet with farmers who had been badly affected by this year's drought.
Prince Harry and Meghan, on their first worldwide tour since marrying in May, also visited the Royal Flying Doctor Service in Dubbo.
After touring Australia, the pair plan to visit Fiji, Tonga and New Zealand. The games, founded by Harry, are an worldwide paralympic-style event for wounded military veterans.