It varies depending on just how much of an individual the soul becomes. At lower levels on the ladder, the group oversoul of the species handles that process and the individual soul doesn't hace to. By the time you get to relatively intelligent creatures such as mammals and birds, the group oversoul still does much of the work but the individual soul starts doing some. Your dog is doing some of it when he's dreaming, just as you do, and the more distinct he is as a personality, the more of it he does. Every fully intelligent species -- humans, dolphins, and so on -- does that sort of work between lives, and after we finish our material incarnations entirely, a lot of work has to go into getting everything sorted out in full consciousness.