According to her article in thepeerage, she was born in 1776 and died in 1791, allowing an approximate dating of this portrait.
From the Christie's Web site.
This dress, hat, and coiffure worn by Lady Beauclerk could have been worn in the 1780s.
Keywords: 1791, Beechey, Georgiana Beauclerk (1776-1791), Beauclerk family, British, long bouffant coiffure, hat, scoop neckline, waist band, natural waistline, wrap, lace, bows