Hmm, I could have sworn that I got permission from Ophelia either in the FAQ here or in a plurk (I've looked in both places, but I can't find it).

I seem to recall it being said somewhere though that domesticated animals survived.

(I might have inferred that from this FAQ answer that mentioned the existence of some animals but didn't specify mutations)

But! If that's been changed or I misunderstood, I'd be open to any suggestions from mods as to how to explain the existence of Nathaniel's dog.