Green’s Dictionary of Slang

rabbit pie n.

a prostitute.

1889–90		Barrère & Leland Dict. of Sl., Jargon and Cant.
c.1904		A. Crowley Snowdrops from a Curate’s Garden 32: By race a full-blooded negress, by profession a threepenny-uprighter, [...] She was as delicious a rabbit-pie as I ever laid this knife to.
1937–84		Partridge DSUE (1984) 953/1: mid-C.19–early 20.

In compounds

rabbit-pie shifter (n.) [? rabbit pie n. or ref. to his appetite]

a policeman.

c.1870

Music Hall Song (S.J. & C.) n.p.: ... vulgar nicknames, such as ‘slop,’ ‘copper,’ ‘rabbit-pie shifter,’ ‘peeler’ [F&H].