Her brother is a young man more than ten years older who has different friends and interests. Even given that he is respectable and principled, his life may be more PG-13 than hers. So, a separate establishment with a companion could be under a different roof at an address removed from her brother.
We don't know exactly how much older than Georgiana is Caroline Bingley. She "keeps house" for her brother when he moves into his new rented estate, and the married sister and her husband come as guests -- along with Darcy. But there is never an indication in the Austen text that Georgiana is "keeping house" for Darcy. Caroline is out, we assume -- meaning she is considered a woman socially who attends parties and is ready to marry. But Georgiana, it seems, is not. So, putting together these clues, I would say Georgiana is not quite old enough to navigate completely in her brother's world quite yet, and her companion keeps her safe in the separate establishment--along with her own servants, including burly footmen guards. Georgiana has her own fortune of thirty thousand pounds, so certainly the interest from that is ample to support her establishment. Darcy probably kicks in to some extent, too, and perhaps he is responsible for Mrs. Annesley's salary? But I am speculating on the fringes. The main point is that separate establishment means not under the same roof as Darcy.
Note, too, that when Darcy and Elizabeth marry, Austen tells us
Quote
Pemberley was now Georgiana's home; and the attachment of the sisters was exactly what Darcy had hoped to see. They were able to love each other even as well as they intended. Georgiana had the highest opinion in the world of Elizabeth;
This suggests that while her brother was unmarried, Georgiana lived separately from him, similarly as she did from her other guardian, Colonel Fitzwilliam.