Hi, AJT - a good place to check for nursery rhymes is http://www.kididdles.com, but I don't see your song there. I do remember something like "doodle-dy-doo," though. If you're looking for books of nursery rhymes with tunes, the "Wee Sing" series is very good.
If you want really comprehensive books of nursery rhymes, chech out the works of Iona and Peter Opie particularly the Oxford Nursery Rhyme Book and the Oxford Dictionary of Nursery Rhymes, and the Puffin Book of Nursery Rhymes. I don't know which of these are in print, but they're all available through www.bookfinder.com