Not sure about a mod for that, but there's a game mechanic that lets your pets live forever as long as you pay attention. The vet's office will have a vending machine that will sell you an Age Down treat. Giving that to your pet will revert it to the BEGINNING of the previous life stage- so, wait for them to turn Elder, then give them the treat, and they will revert to day 1 of Adult. If you give it to them before they age up to Elder, they'll become a puppy or kitten! The baby stage is quite short though.