Kate Middleton

Chris Jackson/Getty Images

The Duke and Duchess of Cambridgedid some good on Good Friday.

Prince William, 31, and Kate Middleton, 32, visited the Royal Easter Show at Sydney Olympic Park. It's one of Australia's largest events, attracting around 900,000 people over the course of two weeks.

Middleton opted to wear a local designer, Zimmerman. The Roamer Day dress, from the Summer/Swim 2014 collection, retails for $495 and arrives in stores this June; it's previously been worn by Naomi Watts. She completed her look with $395 Stuart Weitzman Minx espadrille wedges.

The royals watched a shearing demonstration, and Middleton seized the opportunity to poke fun at her husband's bald spot. Lyn Crejan, a farmer from Glenn Innes in New South Wales, showed them a tuft of alpaca wool that just so happened to be a similar shade to William's hair. "The Prince was interested in the alpaca and as I showed it to them the Princess said he should put it on his head," Crejan told reporters. "She said, 'You need it more than me,' and pointed to his head and he laughed."

MODE/AKM-GSI

They took an impromptu walkabout, and local Kate Swan gave Middleton a book about wombats: "She said, 'I will read this to George. He is obsessed with wombats at the moment. He is really into them.'"

Their Royal Highnesses stroked a 6-year-old ram named Fred and fed him apple pieces. Sheep farmer Jim Murray was elated to show the tourists his farm animal. "He's very intelligent. Sheep are highly trainable if they're treated right," Murray said. "I only found out they wanted him to do this a fortnight ago. The Duke and Duchess were very impressed with his size and stature and how soft his wool was."

While admiring piles of root vegetables in the South East Queensland display, Middleton told preserve maker Diana Lisle that George is particularly fond of sweet potatoes. She also accepted a number of gifts for herself and her 8-month-old son, including handmade chocolates, preserves and baby clothes.

Brendon Thorne/Getty Images

William and Middleton then unveiled a plaque to open the new Southee and Badgery Pavilion. While there, Middleton paid special attention to the photography exhibit. Her Royal Highness told Alison Renwick, former chairwoman of the arts and crafts pavilion, that she enjoys expressing her creativity through art. "She was very interested in the crochet and was brought up by her family and grandmother in particular to appreciate crafts," Renwick said. "Her passion is photography and she likes painting and drawing. I asked her if she still found the time to do it and she said, 'Not very much.'"

The Duke, meanwhile, was impressed with Crejan's pumpkin display. "The Prince was interested in the shine and when I told him I used lacquer he said he'd try it next Halloween," the farmer told reporters.

Later in the day, Middleton toured Sydney's Bear Cottage, one of just two children's hospices in Australia. After meeting staff, patients and families, she called the "inspirational" center as a "haven."

In her speech, Middleton said, "It really is wonderful to be here today, having the chance to meet you all and to see the incredible work of Bear Cottage. First class delivery of children's palliative care is life changing. When families are confronted with the shattering news that their children have a life limiting condition, their world can fall apart. It is at those times that professional support is imperative."

Mark Large - Pool/Getty Images

"I first saw this through East Anglia's Children's Hospices and have since been fortunate to see similar work in Malaysia, then last week at Rainbow Place in New Zealand, and now here today," said the duchess, who is Royal Patron of East Anglia's Children's Hospice. "William and I are strong believers in collaborative work. The sharing of best practice is transformational for organizations. The needs of families requiring children's palliative care across the world are varied. Circumstances and environment can differ, but the aim of those supporting them is the same: to offer the best and most loving care possible."

"I am delighted that Bear Cottage and EACH are planning to be part of a 'community of best practice.' The haven that you have created here is inspirational, and there is so much that you can share with each other as you continue to support and nurture those in your care. If I may, I would also like to take this opportunity to thank everyone who has welcomed me and George so incredibly warmly on our first visit. To be here together as a family has been very special and we will always remember it with fond and happy memories. Thank you for inviting us here and for such a generous welcome."

Chris Jackson/Getty Images

During the visit, the Duke bonded with a 9-month-old local named Max McIntyre, who reminded him of his own baby boy. "I welled up and was really worried I would start crying," William later said.

Middleton participated in a music therapy class-and sang "Twinkle Twinkle Little Star"-and visited the center's quiet room. She later rejoined William for an informal afternoon tea in the center's garden, where the royal couple were presented with artwork painted by the children of Bear Cottage.

Jason Reed - Pool/Getty Images

After their children's hospice visit, the royal couple visited traveled a short distance to Manly Beach. There, they watched volunteers demonstrate their life-saving skills.

The surf community recently revealed that it was crafting a surfboard for George, who was away with nanny Maria Teresa Turrion Borrallo. Middleton told a local she wished her 8-month-old son could have joined them for the afternoon event, but he was asleep when they left to continue the tour.