There are at least three versions of "Kitty Alone" I can think of. The "Froggie Went A-Courtin" version noted above in the first post--which can also be found on the Smithsonian Folkways "Mountain Music of Kentucky" and in this diary excerpt form 1798, which certainly means that this version has been around for at least two centuries. (There are many dozens, probably many hundreds, of variants of the "Froggie Went A-Coutrin'" ballad, though F.J. Child ignored it, somehow.
Another version of "Kitty Alone," which I learned from Howie Mitchell on his Folk Legacy recording, associates the refrain with the "Saw a crow flying low/and a cat spinning tow/Way up yonder, above the moon, bluebird sits in a silver spoon." children's rhyme.
Yet another version, with a different tune, gets sung by the likes of Ed Trickett and Dave Para/Cathy Barton.
The refrain sure does get around, but a couple of centuries of folk processing will do that to a good refrain.