While on location at the beach, the very funny and informative Mary Norris aka “The Comma Queen” offered a rather open-ended explanation about how to properly refer to an animal in terms of relative pronouns such as “who” and “that”.
The point is how you feel about the animal, and there are those of us who are highly fond – we’re very fond of animals and we think they have personalities. And when they’re
named, that they are worthy of personhood and you should use the pronoun who instead of that. But do what you want to do. See what I care. We’re at the beach anything goes.