By about seven to eight weeks old a baby rabbit should be … fully weaned and ready to be separated from its mother. However, do not start this process before at least four weeks of age.Up until then it's vital that they get the nutrition and immunity protection that their mother's milk provides.y about seven to eight weeks old a baby rabbit should be … fully weaned and ready to be separated from its mother. However, do not start this process before at least four weeks of age.