Yes, this is one of the incarnations of the 'music box' or 'musical box', and the Wikipedia article has some information about them:
The original snuff boxes were tiny containers which could fit into a gentleman's waistcoat pocket. The music boxes could have any size from that of a hat box to a large piece of furniture, but most were tabletop specimens. They were usually powered by clockwork and originally produced by artisan watchmakers. For most of the 19th century, the bulk of music box production was concentrated in Switzerland, building upon a strong watchmaking tradition. The first music box factory was opened there in 1815 by Jérémie Recordon and Samuel Junod. There were also a few manufacturers in Bohemia and Germany. By the end of the 19th century, some of the European makers had opened factories in the United States.
Further down is a timeline which explicitly mentions music boxes of this size years before your movie is set:
1800: Isaac Daniel Piguet in Geneva produces repeating musical watches with a pinned horizontal disc operating radially arranged tuned steel teeth.
1811: The first music boxes are produced in Sainte-Croix; an industry which surpasses the watchmaking and lace industries, and rapidly brings renown to the town. At this time, the musical-box industry represents 10% of Switzerland's export.
1865: Charles Reuge, a watchmaker from the Val-de-Travers, settles in Sainte-Croix. He is one of many artisans making pocket watches with musical movements of the traditional calibre.