Green’s Dictionary of Slang

1. (US) a pint bottle (470ml) of liquor; thus short dog, a half-pint bottle.

1908		Denton (MD) Journal 24 Oct. 1/7: Slang of the Sailor Canned beef is known as ‘canned Willie,’ and a bottle of liquor is a ‘dog’.
1942		N. Algren Never Come Morning (1988) 25: I say let’s get half a dog by Rostenkowski’s.
1981		J. Ellroy Brown’s Requiem 29: Toss me another dog, will you?
2013		N. Knight ‘Not Even a Mouse’ in ThugLit Nov.-Dec. [ebook] Max dangled a fresh dog and cracked it.

2. see forty dog under forty n.