There are a heck of a lot of rinky-doodle-toodee-oodum-dees in English folksongs from places where nobody has ever spoken Gaelic. I really doubt if there are more than one or two that started out that way.

I've never met with a folksong idiom that has more nonsense vocables than Kurdish. It has a quite unbelievable number of alternate ways to say "hey nonny no". But there seems to be no nearby culture they could have got that from.