Jack, I'd be interested if you could cite a source or quote the song where the Star of the County Down is a dog.

The song has been much parodied - as in the Belfast based "Star of the Eglantine"

In a snug retreat down in Garfield Street one evening last July,
Down the steps of a tram came a leg like a ham, And she smiled as she passed me by
She looked so fat from the crown of her hat, To her shoes that were size seventeen,
With a musquash coat from a long dead goat And a face like a new wide screen"

There's a chorus which is even less funny.