I took three 7-day vacations back-to-back in my game last RL week to complete the aspirations for OR and JA and to collect the feathers in Brindleton Bay (I have a rental vacay home there). On the home lot I have chickens, 2 horses and a rabbit stump. When I left for each vacation, I got a notice that the horses were being sent to a pet sitter. It was sort of generic as it said that my horses, dogs and cats would be looked after. So, I suspect you'll get the same popup for dogs and cats. The chickens and rabbits were not mentioned.
When I got home after each vacation, everything was fine. The only thing with the horses was they aged the 21 days I was gone but neither had aged to Elder. I have aging set to off in Gameplay Options for the chickens, rabbits, etc. so they didn't age.
So, you can go on a vacation and your pets will only age. I have no idea if they will age up or die if they max the Elder life stage while you are gone. My guess is it will be the same as Elder sims in played households. But I'm no longer sure what happens for Elder sims anymore as I haven't had one that I left behind die while I had the rest of the household on vacation. Originally, they would die within a day of you returning which still might be the case but Idk.
Hope this helps.
