Green’s Dictionary of Slang

(US) a young person who spends the day hanging around shopping malls; a young person who dresses and behaves in a punk fashion.

1984		Eble Campus Sl. Sept. 5: mall punk – someone, usually an adolescent, who dresses and acts fashionably and overly punk without actually being anything of the sort: You can tell a mall punk by the glitter nail polish, the carefully torn Duran Duran shirt, the purple satin tights, and the shades. (Mall punks often run in herds through shopping malls).
1993		G.P. Pelecanos Nick’s Trip 11: I hooked up with her fairly easily through her mall-rat friends and we had lunch.
2006		C. Carr Our Town 274: His sister, Tonia, a blond mallrat in a Notre Dame jacket.