This lovely hat was most likely used for Wuthering Heights in 1992 and retrimmed with black velvet and adorned with ostrich feathers for use in The Duchess. The retrimming and design of the hat is clearly inspired by a portrait of Lady Elizabeth Foster by Angelica Kauffmann, who was, interestingly enough, Georgiana's best friend and husband's lover.
Anrew put his input in with this hat saying "The brim in the Wuthering Heights hat is much larger than the other....the crown is at the same place on both hats, but the front of the brim on the Duchess hat is longer. It's possible that is was cut down, of course, but I honestly think they're two different hats." Thanks Andrew!