Born on January 6, the couple's son Flynn enjoyed a small get-together with family and friends and a sweet surprise from his parents — a cake!

"It was the first cake he had ever seen or tasted. It was a gluten-free cake and organic, of course," Miranda told People magazine.

Talking at her debut as the Qantas ambassador, the model mum, who has spent the last year returning to the catwalk, said her son quite liked his surprise.

"He put his face in the cake. It was a healthy kick-start to his first birthday," she said.

The hands-on mum said she did the cooking for the party and also organized a lot of activities.

"There were a lot of balloons," she said. "We had a balloon man come because [Flynn] likes balloons. That was a lot of fun."

But it seems this one-year-old isn't too keen on partying and after having fun with "five little friends … about the same age," it was time for a nap.

"He was awake for a couple of hours and then it was nap time," Miranda said.

The proud mum also revealed that little Flynn is busy doing something every day and that he is "almost walking". She also said he spends lots of time with his dad.

"He has really stepped up to the role and is very hands-on," she said of her husband.

"It makes me proud that he is such a good dad."