How do you mail a dead rabbit?

Simple (in 1936).  Just put a label on it, and the appropriate postage, and put it in the mail.

In 1936, Post Office rules stated that game, including rabbits, could be posted with nothing but a neck label as long as ‘no liquid is likely to exude’. The postman here is holding some unusual mail found in the Returned Parcels section at Mount Pleasant sorting office, London. 

Photo: Royal Mail Group plc, via The Telegraph.