Here's my version--it is a Scots ditty by the way, or at least I've always thought so. I thought I'd given this to the DT but evidently only the footnotes or something. Anyhow:

There are several versions actually, e.g. this from Robert Chambers' Popular Rhymes of Scotland (1847): Katie Beardie had a coo,

Black and white about the mou';

Wasna that a dentie coo?

Dance, Katie Beardie!

Similarly: ... a hen, Cackled but and cackled ben;

... a cock, That could spin backin' rock;

...a grice [= a young pig], It could skate upon the ice.

Robert Ford in his Children's Rhymes has a cock "That could spin a gude tow rock" and a 5th verse, "Katie Beardie had a wean That was a' her lovin' ain" etc. This last has a variant in Norman Buchan's good little book 101 Scottish Songs (1962), "Katie Beardie had a wean, Widna play when it cam' on rain" etc. Yet another version from Aberdeenshire: Dolly Bairdie haed a coo, Black an' white about the mou, Wasna she a dainty coo-- Dance, Dolly Bairdie.

Similarly: ... a cat, She could tak' baith mouse and rat

... a hen, She could lay baith but an' ben

... a cock, An' he could spin at the hard or rock

... a wife, She could use baith fork an' knife.

There are two tunes to this; one, "Shirramuir", and the other "Whistle o'er the lave o't".