Her cap is just all wrong, Caroline, you're absolutely correct in pointing it out. It's just all over floppy and goofy!
If it's supposed to be a circa 1810 cap, it should look more like this one from La Belle Assemblee. The caul (the portion that fits round the head) should be small and close-fitting, not droopy.
The only sort of loose-fitting caps were mob caps and biggins, and those were only appropriate for informal, at-home-with-the family for breakfast wear. Lady C. wouldn't be caught dead in one of those receiving visitors in the afternoon.
Louisa
Mistress of the Garderobe