Age
We know that Georgiana is 15 throughout the Ramsgate affair, so it’s likely she turns 16 over the course of the novel.
Family and Situation
Georgiana is the orphaned daughter of Mr. Darcy and Lady Anne Darcy, making her the younger sister of Fitzwilliam Darcy. The narrator tells us that for Georgiana, Darcy “had always inspired in herself a respect which almost overcame her affection,” and that it’s a slow realization that Darcy will let Lizzy tease him in ways that he would be less prepared to let Georgiana do. Custody of Georgiana is shared between her brother and her cousin Colonel Fitzwilliam. We never see the cousins together, however, so we have few clues as the nature of her relationship. Georgiana is also niece to Lady Catherine de Bourgh and cousin to Anne de Bourgh, though neither of the de Bourghs ever mention her.
From Wickham, we know that “Since her father’s death, [Georgiana’s] home has been in London, where a lady lives with her, and superintends her education,” though Mrs. Reynolds later tells us that Georgiana is “always” at Pemberley in the summer months. We know that Georgiana has typically had a companion -- this is Mrs. Younge prior to the novel and Mrs. Annesley by the spring. We also know that Mrs. Reynolds has been at Pemberley since Darcy was young, so Georgiana would not remember a time before her.
From her father’s estate, Georgiana has a fortune of £30,000 which makes her a target for fortune hunters, including (former) family friend George Wickham. As Georgiana attempted to elope with Wickham at Ramsgate in the summer prior to the novel, it's likely that she's either very trusting of people or quite lonely.
Other Connections
We have some idea of Georgiana’s social circle. We’re led to believe that Georgiana is fairly close to the Bingleys. Caroline Bingley certainly professes great familiarity and mutual admiration, saying “I really do not think Georgiana Darcy has her equal for beauty, elegance, and accomplishments; and the affection she inspires in Louisa and myself is heightened into something still more interesting, from the hope we dare entertain of her being hereafter our sister.” This same aspiration, we’re told, is shared by Darcy, though it’s unclear how aware of these expectations Georgiana herself may be. Charles Bingley never mentions Georgiana himself, so it’s unlikely there’s particular regard.
Georgiana must also know a Miss Grantley as Caroline mentions preferring Georgiana's design for a table to hers while Darcy is composing a letter at Netherfield.
Appearance
At 15 or 16, Georgiana is still growing into the woman she will be. Based on a conversation between Caroline and Darcy at Netherfield, it sounds as though she is still growing and, by the beginning of the novel, is Elizabeth’s height or a little taller. Lizzy ultimately assesses that Georgiana “tall, and on a larger scale” than herself, noting that “though little more than sixteen, her figure was formed, and her appearance womanly and graceful. She was less handsome than her brother; but there was sense and good humour in her face, and her manners were perfectly unassuming and gentle.”
Character
Though Wickham asserts that Georgiana is “very proud”, like her brother, Elizabeth’s assessment is that she is “only exceedingly shy.” It is with great assistance from kind older women that Georgiana is able to navigate having the ladies over for luncheon and we know that she is ultimately shocked by the liberties that a new Mrs. Darcy takes with her husband (though she later learns to tease).
Habits and Hobbies
Georgiana is praised by most people in the novel as being quite accomplished. Caroline says her performance at the pianoforte is “exquisite.” As of the fall, she is learning the harp and has designed a little table. At Rosings, her brother speaks “with affectionate praise of his sister's proficiency;" he goes on to say that “She practises very constantly.” Described by Mrs. Reynolds as “the handsomest young lady that ever was seen; and so accomplished!—She plays and sings all day long.” We also know that Georgiana’s crayon drawings are hanging on the walls of Pemberley.
