I'm not a lawyer, but I think this is a great example of the beauty of contracts. You can literally make it whatever you want, as long as it doesn't violate the law. There's nothing that forbids you from including provisions for cat care in your lease. And AFAIK, you can even require that your tenants be cat lovers and that they don't have cat allergies, as neither of those groups have anything to do with protected classes.
The only trouble you might have is how you would word your contract in a way that allows you to enforce non-compliance. Maybe a clause that your cat must still be alive and in good health upon your return? But that's up to you.