Duchess thanks Australia for welcoming her and George

The Duchess of Cambridge has described her time in Australia as "very special" as she thanked the country for welcoming her family so warmly.

Kate and William visited a children's hospice in Sydney, where the duchess gave an address on the importance of palliative care for youngsters.

Earlier, the couple attended the Sydney Royal Easter Show, as part of the second leg of their trip Down Under.

William, Kate and Prince George arrived in Australia on Wednesday.

The 10-day trip, which has been the duchess and baby prince's first official visit to the Commonwealth country, followed a tour of New Zealand.

George was not with his parents during their visit to Bear Cottage, which is one of only two children's hospices in Australia.

There, Kate, wearing a white Zimmermann dress, praised everyone from Prime Minister Tony Abbott to the thousands of screaming well-wishers for their greetings since the family touched down on Wednesday.

"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," the duchess said.

"To be here together as a family has been very special and we will always remember it with fond and happy memories."

In her speech to children, staff, supporters and parents at the hospice, Kate described the first-class delivery of children's palliative care as "life changing".

The duchess, who is a royal patron of East Anglia's Children's Hospice (Each), visited a hospice in Malaysia and last week another in New Zealand.

She said when families were confronted with the "shattering" news that their children have a life-limiting condition, their world could fall apart, and that professional support was therefore "imperative".

"The sharing of best practice is transformational for organisations," Kate added.

"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."

The royal couple also visited Sydney's Manly Beach, where they were shown demonstrations by surf lifesavers.

Earlier, they attended the prestigious Sydney Royal Easter Show - an agricultural event billed as one that "brings the country to the city".

The 14-day event, which attracts more than 900,000 visitors every year. features prize-winning livestock, from beef cattle and merino sheep to horses and goats.

Other animals make an appearance, such as lizards and alpacas. Visitors can also take part in pig patting, chuck washing and cow milking.

The duchess, upon seeing a tuft of alpaca wool joked that William could use it to cover his bald patch.

Exhibitor Lyn Crejan showed the pair the wool as she talked them through a display of fruit and vegetables.

The 67-year-old farmer, from the settlement of Glenn Innes in New South Wales, said: "The prince was interested in the alpaca and as I showed it to them the princess said he should put it on his head.

"She said, 'You need it more than me,' and pointed to his head and he laughed."

William and Kate were also greeted by a well-mannered ram named Fred, who bowed to them as they arrived at a sheep-shearing display.

The six-year-old merino ram went down on one knee with help from his owner Jim Murray.

A delighted William and Kate stroked Fred and gave him some treats.

"He's very intelligent, sheep are highly trainable if they're treated right," Mr 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."

On Thursday, William and Kate toured the Blue Mountains region near Sydney, where they took in the sights and met people whose homes had been destroyed in devastating bushfires last year.

The couple, along with baby George, will spend 10 days in Australia, visiting its famous sites, honouring its war dead and meeting locals.

They are expected to bring the prince to Taronga zoo in Sydney on Sunday where an enclosure housing bilbys - a rabbit-like marsupial - will be named after him.