The story
First use appears c. the 1960s. Possibly of German origin, in the sense (cute or loveable) as a form of endearment for children; also may have a connection to the Scottish term "pook" (to pluck, peal) and the term from the cartoon Garfield, where the main character Garfield has a teddy bear named Pookie.
Etymology from Wiktionary, CC BY-SA 4.0.