Despite what Regency authors often write in their novels, it was not a requirement that any one be presented to the queen before dancing at Almack's or being considered "out." Some of the patronesses of Almack's felt they were more exclusive than court, giving and denying permission almost at whim only young ladies of spotless character and connections. A girl could have any number of seasons before being presented to the queen. Some never were presented until after they married. Of course, not attending a drawing room could imply that if the family had money problems; those gowns combining the feathers and hoop skirts of the Georgian era with the high waists of the Regency era thereby making a lady's figure look as terrible as possible were expensive and couldn't be worn anywhere else!
Only the daughters of peers would have been presented at Court when the queen held her "drawing room" for that specific purpose. There's a great book about this topic, "GILDED BUTTERFLIES: The rise and fall of the London season" by Philippa Pullar. By the way, the term debutante is Victorian, so it was never used during the Regency period.
The girls could attend social gatherings before being presented. When a young lady was about the right age, normally about 17 or 18, her mother sent in a notice to the Chamberlain that she wished to present her daughter at the next “drawing room.” The chamberlain sent her the date and a list of requirements as for dress and number of feathers.
In Gilded Butterflies, Pullar says that court required feathers as soon as society decided they didn't want them any more. The girl went with her mother on the proper day. The queen kissed the daughters of the peers. She often spoke to them as well. All brides of peers and men who attended court had to be presented as well, even if they had been presented before marriage. Also the wives of the diplomatic corps were presented.
April 30.1812 “The Queen held a drawing room at St. James's Palace. It being the first which her Majesty has held since the King's birth day in 1810, and there having been no Court for the ladies during a lapse of nearly two years, great preparations were made by the higher ranks for their appearance on this occasion.”
Though Queen Charlotte scheduled drawing rooms fairly frequently up until 1811, after that date they were irregular and spread apart. The sponsor-- the female who was sponsoring the girl -- the sponsor had to have already been presented herself, of course-- inquired as to the next drawing room and asked permission to present the girl ; she had her name and the name of the girl listed with the Lord Chamberlian's office. This office would send out the invitations and the information as to what people were supposed to wear to those who had requested permission for a presentation. At the presentation the girls went forward as called out. She knelt to the queen. The queen kissed the daughters of peers on the forehead but gave her hand to be kissed by anyone else. The girl then stood and backed away from the queen. She could not look behind her and could not turn her back on the queen. Then they usually went home.
Queen Caroline never gave drawing rooms. It was always Queen Charlotte who did it until her death in 1818. Then the Prince Regent/George IV had his sisters hold the drawing rooms.