US copyright laws have changed over the years, but prior to 1976, copyrights only lasted a maximum of 56 years. After that, a design went into the public domain and anyone could use it freely. Therefore, if the museum dress was made prior to 1920, you're probably quite safe in copying the fabric.
Note that this only applies to the USA. Other countries have different laws. If you have any doubts at all, it's best to consult with a trademark/copyright lawyer. (Reminder: I am not a lawyer!) This is especially true if you plan on selling your fabric--you don't want to risk getting in trouble over a copyright violation.
The timing of this article could not possibly be better! I spent four hours last night searching for something even vaguely similar to the fabric in my head... to no avail. You're a lifesaver!
I'm glad you found the article useful! Be sure and come back for the second half, as it will explain how to create more complex fabric designs, as well as how to avoid problems with tiling, wicking, and color differences when printing your design.
Genius article! I've been wanting to do this for the past year but had no idea how. And I just sent the link of the GWTW bbq fabric to my friend, she's been dying to have that dress made for ages. Thanks!