All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The matter in this regard is easy, as you may sell this rabbit, give it away, or slaughter it and eat its meat or give it to someone else to eat. A rabbit is among the animals whose meat is lawful. The evidence is that some Companions ate it and gave some of it to the Prophet who accepted it. Imaam An-Nawawi said: “Eating the rabbit is lawful according to Imaam Maalik, Abu Haneefah, Ash-Shaaafi’i, Ahmad and all the scholars….” For more benefit, please refer to Fatwa 84598.
Also, it is permissible for you to let the rabbit free and you are not sinful; one would be sinful if he/she keeps it in a cage and does not give it food and drink until it dies. This is the case where the sin and threat apply in the Hadeeth of ‘Abdullah ibn ‘Umar who said: the Prophet said: “A woman was punished and entered Hellfire because she kept a cat in captivity until it died, she neither fed it nor gave it water to drink; nor did she set it free so that it could eat from the vermin of the earth.” [Al-Bukhari and Muslim]
Allaah knows best.