Catherine met Bailey Rupe at a children's hospice on the latest leg of the royal tour of New Zealand.
She was met by more than 40 children and their families at Rainbow Place in Hamilton.
"There should be more places like this," AFP quoted her as saying of the facility, which provides support for children affected by serious illness.
It was the duchess's first solo engagement on the 19-day tour which will also take in Australia.
Children at the hospice explained how the facilities help them express their feelings 
The Duchess of Cambridge is a patron of East Anglia's Children's Hospice back in the UK 
The duchess met children of all ages during her visit She met youngsters and parents and had a briefing with the hospice's chief executive before going to a Mad Hatter's themed tea party.
Six-year-old Bailey, whose mother was given six weeks to live, showed the duchess how she uses puppets to express how she feels about her mother's illness.
'Real princess'"Are you having tea? Can I sit with you? How is mummy doing?" Catherine asked her.
"Do you find it difficult sometimes? Yes, I'm sure you do, but you're a very brave little girl."
Bailey said afterwards: "I was excited to meet a real princess and it made me feel like a princess for the day too."
Prince William, meanwhile, was shown around Pacific Aerospace, an aviation firm in Hamilton.
He was told about the P-750, an innovative light aircraft made at the plant.
The prince was shown inside Pacific Aerospace's P-750 light aircraft "He talked about his friendly brotherly rivalry, with Harry flying Apaches and he's been flying search and rescue," the company's chief executive Damian Camp told reporters.
"He said he still does some flying - all helicopter based - but not as much as he wants to."
William spent more than seven years in the military and was presented with his RAF wings in 2008.
Mr Camp added: "He said George has settled into a nice routine but was keeping mum and dad on their toes but they're all enjoying their stay."
The couple later reconvened in the nearby town of Cambridge where thousands of well-wishers lined the streets to greet them.
The duke and duchess each left a single red rose at a local war memorial as they paid their respects to New Zealand's war dead.
Prince William was joined by Catherine on a walkabout in the aptly named town of Cambridge on Saturday 
The couple each placed a flower on the war memorial at Cambridge Town Hall 
Thousands of royal fans crowded the streets of the town centre in a bid to catch a glimpse of the couple 
Although there was at least one person who did not share their enthusiasm They also opened a new velodrome in the town and met some of New Zealand's cycling, rowing and canoeing elite.
"I know what a special place cycling holds for New Zealanders and what a beneficial and thrilling sport it is," Prince William told spectators.
The couple were handed a tiny cycling jersey in the country's colours for Prince George, who is not with his parents for this part of the tour.
The tour is the first official visit for eight-month-old George 
Prince George was not present on Saturday - but still received plenty of gifts But even in his absence the young prince was given another gift - his first bike and crash helmet.
The cycling-themed presents will be added to those he has already picked up on the trip, which include a miniature amphibious boat.
"I hope they don't get excess baggage [charges]," joked John Struther, who founded the Avanti bike company which is behind the bike model.
The tour has so far seen the royals race yachts, attend a state reception and visit a parent and baby class with Prince George in New Zealand before they head to Australia later this month.
The trip is due to end on 25 April in Canberra.
