But her successor Kevin Rudd has upped the ante on the royal gift front, announcing the new ''bub'' will not only get a toy bilby but a free pass to Taronga Zoo, among other acts to honour his birth.

Speaking to reporters in Melbourne on Tuesday, Mr Rudd said that he had been talking to his wife Therese and daughter Jessica about what to give the royal baby, who was born Monday afternoon London time.

He said the Australian government would also be sending a copy of Mem Fox's book, Ten Little Fingers and Ten Little Toes.

''We'll be providing a copy of that wonderful Australian children's book to the mum and dad to read to the bub.''

Mr Rudd said he had also been thinking about ''what works a bit more over time''. In honour of the Royal family's commitment to the environment and conservation, the federal government would donate $10,000 to a bilby preservation program at Taronga Zoo.

Mr Rudd said the bilby was ''one great Australian marsupial which is in a bit of strife at present''.

The Prime Minister also said that if Taronga Zoo agreed, the bilby enclosure would be named after the as yet unnamed prince.

As well as a ''cute and cuddly'' toy bilby for the prince, Mr Rudd said the royals could also expect free zoo access.

''I don't know if the royal family would need this but we'll probably give them a free pass to Tarogna Zoo as well.''

A zoo spokesman said zoo staff were proud that Australia's gift to the royal couple recognised the threatened animal.

A plaque will be placed at the bilby exhibit to acknowledge the gift, and the spokesman said the zoo agreed with Mr Rudd's suggestion about naming the enclosure after the prince.

"We're looking forward to being creative about that when we know the new prince's name," he said.

Before Ms Gillard was removed from as prime minister she was photographed in the Australian Women's Weekly knitting a stuffed kangaroo for the royal baby.

Ms Gillard's office had no comment when asked on Tuesday if the knitted kangaroo had been sent to the Duke and Duchess of Cambridge. However, a source close to the former leader said she may still send the toy.

New Zealand's Prime Minister John Key said the country's official gift would be a lace shawl, similar to the one the country gave Prince William when he was born.