In a second photograph, she appears to be gazing past the camera as if something has caught her attention in the background.
It is the first time Princess Charlotte has been seen in public since July, when she was baptised at St Mary Magdalene Church on the Queen's Sandringham Estate in Norfolk.
The pictures show the Princess growing rapidly, inheriting her mother's dark brown hair, while her bright blue eyes are striking, similar to those in pictures of her father, Prince William, taken at around the same age.
It is the second time in recent months in which the Duchess, a keen amateur photographer, has released images of her children.
While the happy, informal photographs, and the decision to share them on social media, will strike a chord with any parent in the Facebook generation, they also carry echoes of a long line of royal portraiture.
Historians said that, in particular, the presence of the toy dog fits into a tradition going back at least to the time of Charles I. Pets have been a regular feature of royal portraits, particularly with younger members of the family, since the 1630s, when Van Dyck painted the three eldest children of Charles I standing between two spaniels.
Moving into the photographic age, Queen Victoria's beloved Pomeranian dogs become a prominent theme in imagery in her later years.
Princess Charlotte's picture bears a particular resemblance to a photo of the current Queen, then Princess Elizabeth, in May 1927 with a toy tiger. The Daily Telegraph
