Then there is Tintin's terrier, Snowy, and Obelix's Gaulish dog, Dogmatix, in Asterix comics, but they didn't have comics of their own. Come to think of it, Dogmatix did have a small comic book of his own.
I have left out animals from comic strips like Fred Basset, Marmaduke, Hobbes, Garfield, and Dennis the Menace's Ruff, perhaps, in another post.
I can't help thinking I've left out some obvious names. If you can think of any, let me know.