At this point it's not clear whether there are two songs we are after, one about Kitty and one about Willy, or just one, with the name varying maybe (whicy I suspect is probably the case).
Either way, there's at least one first rate song in need of tracking down. So far as Kitty is concerned, South Africa sounds as if itws where to look - no luck so far, though I found this site , with some great Nursery Rhymes in Afrikaans with English translations.
If I find anything I'll report. But don't leave it to me, if you've any ideas/