Andy:
No, the dress Edith wore off the ship is not in a museum. Unfortunately the suitcase it was in, when she returned from her last trip to the USA in 1953 (to attend the premier of the movie Titanic), was mishandled and lost.
However, the photo above shows what it looked like and she also described it over the years in interviews, including one with John Maxtone Graham in the early 1970s. She said it was brown.
In most of her articles, Edith refers to the outfit she wore as a "hobble skirt," whereas it was actually a dress, although the skirt was of the "hobble" variety, meaning it was tapered. It was not a classic "hobble" or ‘sheath" skirt but one of the newer versions, being draped and gathered.
The picture shows that Edith’s dress consisted of a tunic (or overdress) of taffeta, trimmed in lace, ribbon and ornamental buttons, and a skirt of cloth or light wool that is draped up on one side. The hem of the skirt isn’t visible in the picture but it would have reached to the instep or ankle. This type of costume, blending a rich material and a simpler one, was all the rage in 1912, especially in the collections of Paris designers Bernard and Paquin. Edith was bringing over quite a bit of merchandise from these two couturiers, so the dress was probably made by one or the other.
Randy