Green’s Dictionary of Slang

(orig. US) to run errands, to go out for something.

1954		in V. Randolph Pissing in the Snow (1988) 148: There was a bunch of Pukes lived over by Joplin, at a camp knowed as Minersville. The boys [...] just gophered around in prospect holes, because there wasn’t no powder to speak of.
1964		Larner & Tefferteller Addict in the Street (1966) 85: You tell a fellow you’re a gopher. You know the pusher and you’ll gopher narcotics.
1986		F. Taylor Auf Wiedersehen Pet Two 18: Go-fer the golf clubs, go-fer the wife. Go-fer the sodding dry cleaning.
1990		S. Morgan Homeboy 64: Rooski [...] was too sick for any more gofering just now.