Vintage Fashion Guild posted the painting of a milliner wearing that exact outfit as an example of hats in the 19th century. It is undoubtedly the forebear of Ms. Garland's distinct dress. However, the signature on the painting is so illegible that for years the name of this artist eluded me. It wasn't until Ikranieri at the VFG forum identified the portrait this year that the search finally ended.
Charles Philipon is famous for having co-founded and illustrated a satiric magazine -La Caricature- in Paris, which ran from 1830 to 1835. The Pirate's storyline is set, not in the same place but in a similar time frame: "a small village in the West Indies early in the 19th century," according to the movie's predecessor, S. N. Behrman's play of the same name. The painting of the milliner is apparently part of a series that Philipon completed at his leisure - "Occupations d'une femme" (1827-1830).
Keogh dresses Ms. Garland's character, Manuela, as Philipon's milliner. Perhaps he is inferring that she has seen the painting somehow, despite never having left her small town, and has sewn a copy of the dress. She's that infatuated with any place but home.
Or perhaps it's not that literal. Manuela has Paris on the brain; the gaiety and wonder of the French capital is a symbol of escape from "this little saucer in the hills." Maybe Keogh is simply giving this character a taste of what she wants without her knowing it. The designer is simply underscoring the idea that while other young ladies wear a more regional headdress and skirts (highlighting their contentment at home), Manuela's dress represents a distant land that's on her mind.