ETYMOLOGY
apparently a derivative of dandle (to move (a child, etc.) lightly up and down in the arms or on the knee)
EXAMPLE
“… I wes in youthe, on nureice kne,
Cald dandillie, bischop, dandillie,
And quhone that age now dois me greif,
A sempill vicar I can nocht be:
Exces of thocht dois me mischief. …”
From: Dunbar: A Critical Exposition of the Poems
By Tom Scott, 1965
Don is a Battell on the Dragon Blak
Composed by William Dunbar, a1513
Lexicophilia 