Judging by the American PDQ I'd say quick can be an adverb in American English. As a youngster I was taught that it stands for pretty damn quick although I suppose it could just as well be pretty damn quickly.
I've always thought of PDQ as meaning 'pretty damn quick', where quick is an adjective, modified by the adverbs pretty and damn. But I think probus has a point when he says that the entire expression can be used adverbially:
She finished it pretty damn quick.
Whether such use is considered acceptable standard English or not I think is a matter of opinion.