This is one of the various small animals found on the Sto Plains or on the pathways and roads, as well as in various gardens around the disc.
Features of Rabbits
You can, when holding a knife, get parts from the corpse of a rabbit.
The eyes can be used in a Wizard's spell. Pragy's Fiery Gaze.
The skin or fur or hide
Vic, the tanner in Ohlan Cutash buys animal hides. You can then use the money to buy armour, clothing, etc.
There is a tannery near the Genuan embassy in Ankh Morpork that also buys hides.
There is a furrier in Mad Wolf that will make custom fur items. He might buy hides, too. Never tried it there but the help here lists sell as an option.I think it could just be wolf hides.
You can also sell the entire corpse of an animal in the Butchers' guild in Ankh Morpork . There might be some restrictions on what corpses they take. I have only ever tried chickens, but other animals, such as rabbits, may well work.
You may need to pickle the corpse/body part, either by using a player shop pickling machine, or a wand made from Colltrap's Instant Pickling Stick which you hold and 'zap'. Corpse parts eventually disappear if not pickled.