Muslims are permitted to hunt lawful animals and birds which cannot be easily caught and slaughtered, including non-meat eating animals such as deer and wild rabbits.
Allah has laid down a number of rules relating to eating and drinking, which generally serve to realise certain divine purposes, such as reminding people of Allah’s bounty upon them, protecting them against diseases and avoiding extravagance and pride.
The prophet said, “Allah is pleased with a slave of His who eats something and praises Him for it and drinks something and praises Him for it.” (Saheeh Muslim: 2734)