She was a daughter of William Pennell, British Consul-General in Brazil, but was adopted by the politician and man of letters John Wilson Croker (1750-1857), and took his surname. At the time when this portrait was painted she was only 17. Evidently intelligent and well-educated, she worked for Croker as a secretary, and later married Sir George Barrow, a distinguished civil servant who worked at the Colonial Office. This is a detail showing the masterly portrayal of the expression on her face; she evidently made quite an impression on the painter, and this surely one of his most memorable portraits.
Some interesting material about the sitter and her portrait here:
Croker was a friend of George IV, who was fond of children and was very taken with the young Rosamond, so that she became a familiar figure at court. She was a niece of Croker's wife, and the adoption had been arranged to console her after she had lost her own child (the Pennells had so many that they were happy to agree).