Green’s Dictionary of Slang

1. to scrounge [naut. jargon rabbit, a smuggled/stolen article; note N.Z. use (post 1950) which comes from the image of a rabbit attacking the tops of root crops].

1943		Baker Popular Dict. Aus. Sl. (2nd edn) 63: To rabbit, to borrow, ‘scrounge’. (R.A.N. slang.).
1953		K. Tennant Joyful Condemned 198: Why were Australian Navy men better at ‘rabbiting’ little valuable articles than Americans.
1955		N. Pulliam I Travelled a Lonely Land (1957) 237/2: rabbit – [...] to borrow.

2. to leave quickly, to run away.

1937		E. Anderson Thieves Like Us (1999) 24: Things started getting hot and he rabbited for Mexico.
1953		T. Runyon In For Life 153: I didn’t get a chance to turn rabbit.
1969		‘Iceberg Slim’ Mama Black Widow 57: Ain’t no use tu rabbit outta’ here.
1975		J. Wambaugh Choirboys (1976) 23: This black ass, abba dabba motherfucker looked like he was gonna rabbit.
1986		C. Stroud Close Pursuit (1988) 286: His disappeared through a back door. Shit, thought Kennedy. he’s rabbited.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 337: The old girl saw him and rabbited – a run for the door.
1990		S. Morgan Homeboy 21: Had a father I never told you about once played rabbit from the Federales.
2004		J. Ellroy ‘Jungletown Jihad’ in Destination: Morgue! (2004) 341: We left Camel Cal [...] He might rabbit or free-form freak out.
2010		Codella and Bennett Alphaville (2011) 228: The guy Frankie pointed at looked like he was going to rabbit.