The song ties minstrelsy and mumming plays together. Mumming plays were held in people's kitchens and so were the original minstrel entertainments as Thomas Rice's "Clare de Kitchen" (1832) would demonstrate. So someone being in the kitchen with Dinah strumming a banjo is another reference. A black minstrel performer and writer named James Bland ("Golden Slippers") wrote a piece in 1880 called "Dancing on de Kitchen Floor." One verse goes:

Oh, the darkies all will have a jubilee
Such a gathering there never was before
Oh, happy everyone will be
As we dance upon the kitchen floor

There is an 1890 stereo-card called "Dancing in the Kitchen" showing five men—all in blackface, two dressed as women—singing and dancing in a kitchen. One man plays a banjo and the other, in suit and top hat, plays a fiddle. The fiddler is the only one seated.

In the Nast engraving below, we see Santa dancing with Mother Goose. We also see the cat with a fiddle, the little dog laughing, the cow jumping over the moon, the dish and spoon cavorting together but the whole thing is portrayed as a minstrel performance and appears to be going on a kitchen.

http://imagehost.vendio.com/preview/ha/haats/HW1880P1977.jpg