Green’s Dictionary of Slang

(US) to play truant; thus do/make like a paper doll and cut v., go away.

1943		D. Burley N.Y. Amsterdam News 9 Oct. 20: I was [...] doing a paper dolly at the knowledge stash.
1944		‘Jiver’s Bible’ in D. Burley Orig. Hbk of Harlem Jive.