Royal baby Prince George has upstaged his parents at just his second public engagement – playing with bilbies at Sydney’s Taronga Zoo.

It was the picture perfect moment the world had been waiting for.

Royal baby Prince George giggled, smiled and played his way through just his second public engagement – a trip to the zoo with his parents Prince William and Kate on Sunday.

The trio arrived at Sydney’s Taronga Zoo to visit the bilby enclosure named after Prince George as part of Australia’s gift marking his birth on July 22 last year.

It was just the fifth time the royal tot, who is almost nine months old, had been seen in public on this trip.

Dressed in royal blue shorts and a striped, light blue shirt and blue shoes and socks, he appeared to wriggle mischievously in Kate’s arms as the family strolled to the bilby enclosure.

For much of this royal tour of New Zealand and Australia, the eyes of the world have been trained on Kate and her fashion choices.

For the zoo, she had changed out of the dove-grey Alexander McQueen outfit she had worn to an Easter church service, into a lemon cream broderie anglaise dress.

At the enclosure, George met a bilby – also called George, then helped his parents unveil a plaque, renaming the enclosure the Prince George Bilby Exhibit.

Bilby keeper Paul Davies said the royal couple were relaxed with George inside the enclosure.

“All of a sudden they were just a family in the zoo,” Mr Davies said.

He said at one point George wanted to grab the bilby’s ear.

“I said ‘he can touch the bilby’, but they said no, he (the bilby) will have one ear less,” Mr Davies said.

After the bilbies, George returned to Admiralty House and William and Kate viewed other animals at Taronga.

They fed tree kangaroos, strolled past giraffes, enjoyed a bird show, and took in the rhino conservation display.

At the bird show, the couple had galahs and owls swooping just centimetres above their heads.

Taronga Zoo bird trainer Brendan Host presented the bird show, before introducing the duke and duchess to two echidnas, a quokka and a koala named Leuca.

“I think Kate was very taken with Leuca,” Mr Host, 27, told reporters after the show.

“She didn’t realise the koala would smell the way it did because they eat eucalyptus leaves.

“I think she just really enjoyed the moment.”

The royals posed with Leuca and the echidnas with iconic Sydney Harbour Bridge and Opera House in the background.

This was Australia – as much as the royals – on show.

As he touched the koala, William commented: “This is the moment everyone’s been waiting for.”

The couple also heard about a number of Australia’s endangered species at the bird show – and appeared to take a keen interest.

Taronga Zoo volunteer Meghan was in the audience at the bird show and said the duchess looked “incredible”.

“She’s stunning, she’s perfectly put together, there’s never anything out of place.”

Michael, 49, at the zoo with his three-year-old son Jimmy, described George as “quite a handsome little man.

“And the duke and duchess; they’re a beautiful couple of course.”

He said Jimmy “wanted to have a little bit of a play” with the young prince, adding that he hoped the royals had a “great day out” at the zoo.

The duke and duchess finished their tour at the rhino conservation area and the Taronga Wild!, a mass public art exhibition and community conservation initiative raising awareness and support for Taronga’s black rhinoceros breeding program.

They also met John Scanlon, secretary-general of the Convention on International Trade in Endangered Species of Wild Fauna and Flora.

“The duke speaks passionately about his child – Prince George – having the opportunity to see these animals in the wild,” Mr Scanlon said afterwards.

“He’s very passionate and engaged in this issue.”

In February, William attended a high-level summit on the illegal wildlife trade in London alongside his father Prince Charles and brother Prince Harry to ensure the “survival of some of the world’s most treasured species” and set up his own initiative, a wildlife charity, United For Wildlife.