Sometimes I get lucky and there are sheep and cows everywhere near spawn. Other times I have to search far and wide for them. You seem to have settled in an unlucky spot. I would harvest some wheat, lure cows and sheep to my base and breed them. I always have cow, sheep and chicken pens near my home. I don't pay much attention to rabbits and don't see many except in deserts. Maybe they are just more visible there because there is no foliage for them to hide in.