We have probably had this picture about 30 years. It is a reproduction print but we cannot now recall who the little girl is, her name being hidden by the old picture frame we put the print in. Our recollection is that she might be Spanish (perhaps an Infanta?) but if anyone knows more do please let us know. Like a few other prints and photographs round the house the reds and yellows have faded over the years, so that she has now begun to withdraw gently into the blue misty distance. Nevertheless we are both very fond of her.
Update: Maria very kindly checked for Spanish sources (see her post below) for the picture and found none, suggesting that the portrait originated elsewhere. At the same time a friend of ours who lives nearby emailed to identify the little girl as Italian, probably Bia (or Bianca) de Medici. The painting is by Agnolo Bronzino. Her Wikipedia entry says she was the illegitimate daughter of Cosimo I de Medici, Grand Duke of Tuscany. The identity of Bia’s mother is not known, but Cosimo I was probably no older than sixteen when he fathered her. She was described at the time as a very affectionate, high-spirited, loving little girl. She died of a fever on 1st March 1542, after an illness lasting several days. She was aged about six.