Green’s Dictionary of Slang

(US campus) fashionably dressed, also as v. to dress fashionably.

1981		Eble Campus Sl. Fall 3: GQ – distinctively dressed.
1986		C. Stroud Close Pursuit (1988) 243: Fratelli was looking extremely ‘GQ’ today [...] he had his navy-blue Gianni Versace on today, with a wrinkle-shirt to match, and a linen tie.
1995		L. Stavsky et al. A2Z 43: GQ B-boy – a rapper who wears slick silk suits, argyle socks and loafers.
2012		W.D. Myers All the Right Stuff 111: My cousin was looking sharp. [...] My man was GQing all the way.