The Duke and Duchess of Cambridge, along with Prince George, head to the next stop on their tour Down Under after a busy visit to New Zealand

Prince William, wife Kate and little Prince George waved goodbye to New Zealand and prepared to say g’day to Australia.

The young royal family ended their exciting stay in New Zealand Wednesday by stepping on an Australian air force plane to Sydney.

The couple had spent their last full day, Tuesday, in New Zealand privately, enjoying some family time with 9-month-old George by remaining on the grounds of Government House, which had been their main residence during their stay in the country, a palace source tells PEOPLE.

Early Wednesday, they visited the Royal New Zealand Police College, which was originally opened by the 31-year-old Duke of Cambridge’s dad, Prince Charles, in 1981. In a final nod to New Zealand fashion, Kate, 32, was wearing a skirt suit by one of the country’s leading designers, Rebecca Taylor.

During their last engagements in New Zealand, the couple got to indulge in some puppy love: They were introduced to a pair of 12-day-old puppies from the police Dog Training Centre.

As she picked up one of them, Kate said: “It wants to hide under my jacket. I think it can smell George.”

Soon after they arrive in Australia, the duke and duchess are expected to begin their nine-day stay with a reception for young people at Sydney’s iconic Opera House.