Interesting, since cats are the one domestic animal that definitely was extant there/then that is NOT mentioned in the Bible.
That has to say something about ol' Illiterate Moe and his rambling (purported) writings.
Some how, some way, his own personal feelings regarding dogs and cats just got involved in his religion.
I do remember some kind of referance to him having a woman stoned for killing a cat, and his, eventually made some kind of exception for "working dogs". Though, considering the time frame then, I have no idea what that means, and Mohammad himself doesn't explain it.
Who knows, maybe a dog bit him as a kid and he held a grudge, either way, he really really hated them.