Bonjour Joakim ! In French, you could use either, with a slight nuance of meaning: "On ne mange pas de lapereau." would mean "We don't eat baby rabbit" in general, as a type of meat here. If you consider the baby rabbits as countable elements, then you could also use the plural: "On ne mange pas de lapereaux." I hope that's helpful!

"un"and "une" also become "de" in negative sentences, see: Un, une become de or d' in negative sentences (indefinite articles)