― Question by ManiF: Can rabbits make good pets? Do they follow their owners around or be affectionate to them? Also, can rabbits have personalities too? If you want a rabbit as a pet, can they be warm and affectionate or even playful? Can an elderly person have a rabbit or is it too much work? Best answer: Answer by CrisWell, it sounds like you are looking for a dog. Rabbits are like cats in a way do there own thing. They are soft and if you bring them to you you can cuddle up with them..... [...].