Green’s Dictionary of Slang

(US) a rowdy; a young hoodlum.

1859		Matsell Vocabulum.
1882		Breckenridge News (Cloveport, KY) 23 Aug. 3/3: With a smart ‘peddler’s pony’ swinging in my hand I was as fancy a ‘rabbit’ as walked the street.
1927		(con. 1820s) H. Asbury Gangs of N.Y. 22: [note] In the slang of the period a rabbit was a rowdy, and a dead rabbit was a very rowdy, athletic fellow.