Not really. Pre self reading age, I remember Peter Rabbit with Flopsy, Mopsy and Cottontail, but I got hooked very early on Jack London and Charles GD Roberts and subsequently had an aversion to any animal story in which the animals wore clothes.
Could be the reason why, much later, I did enjoy Watership Down, but I'm still at a loss why people read it or show the movie Watership Down to very young children, its frightening for them. Then again, in most of the animal stories I read when small, the animals usually met a somewhat natural, violent death and I usually spent my reading time bawling my eyes out.....over and over and over again. LOL