Muslin was an incredibly fashionable fabric in late eighteenth-century Europe, particularly France. Jane Austen's characters often wear muslin gowns; Catherine Morland's first conversation with Henry Tilney in Northanger Abbey is about sprigged muslin.
Caribbean Creole fashion was heavily influenced by French fashion, although it lagged somewhat behind. Muslin is a particularly breathable fabric, and relatively well suited to the heat of the Caribbean.
The picture shows fashionable muslin ball gowns from 1838, roughly contemporaneous to the time this section of the novel is set, though they are rather more ornate than the gown Antoinette is likely to have worn.