Carole Middleton, her mother, took the photograph.
The post is part of the Shaping Us initiative, which seeks to raise awareness about the influence of childhood on adulthood.
The initiative promotes the sharing of childhood images and the discussion of early childhood memories.
She gave a significant London lecture and released a clay animation short to encourage early childhood.
Kate went to Leeds Kirkgate Market to talk about the early years with vendors and members of the public.
The campaign has the backing of Royal Foundation "champions" such as Giovanna Fletcher and Zara McDermott.