[Cats and Dogs] Can I make my pet die of old age (or of anything really) with aging off?

There might be a treat for it in the vet's vending machine.

Well, the only way I can see the way to do that is this:
Download TwistedMexi's mod that allows all the cheats that were disabled in Seasons patch, then enter this cheat:

sims.get_sim_id_by_name   (I have found it working when the pet doesn't have a last name)

You'll get the pet's simID. Turn the aging on for a moment and enter this cheat:

sims.age_up 

Elder pets should then die by old age while younger pets age up.

There is a pet age up treat that can be bought in a vet clinic, but it cannot be given to elder pets.
So I really don't know any mod-free alternatives. We can ask the developers to unlock/add a cheat that ages up sims and pets.