Turning off aging is the best option. Be forewarned that this will prevent hatched chicks from aging up as well. I'm mostly ok with this, as I like having a rooster, a few hens, and a few chicks. But when I have needed to age some of them up, I turn aging back on, and then turn it off again as soon as they age up.
If you want to be extra-careful, you could do that and *also* give the ownable livestock healthy treats (I think these are the ones that extend their lifespans), so that even if you have periodic aging days, it will take a very, very long time for them to live out their lives. The only thing this won't necessarily help with is if you have elder bunnies and elder foxes right from the start, they may not make it, because I don't think you can give them animal treats. But turning aging off most of the time will still buy you some time before they pass.
