ETYMOLOGY
apparently a random formation, possibly influenced by doodle (n.) and perhaps also fopdoodle (n.)
EXAMPLE
“…But to look for such things from a revengful mind, is as unlikely as to make the bristly skin of a Hedghog smooth. And when all the Stuff in the Letters are scann’d, what Fadoodles are brought to light?…”
From: Scrinia Reserata a Memorial Offer’d to the Great Deservings of John Williams
By John Hacket, 1693
Lexicophilia 