Will animals come with us to space?

When we are forced to move on from earth will animals be able to come to a new planet with us? Like dogs cats birds fish and what about larger animals or exotic animals elephants crocodiles ext. We will want to bring them with us for sure and most likely if our new host planet could support us freely like without oxygen tanks and other artificial stuff to keep us alive they should be able to to right? What type animals wouldn't be able to come?