You should have multiple back up sitters available in case your primary sitter is taken up in the Rapture.
You'll also need some kind of system to alert them that you've been taken up. You'll probably need to have some kind of prepayment plan, since you won't be around to write checks.
For advice on picking a pet sitter, check out Evaluation
Pet Food
You'll need some kind of auto dispenser as well. The Rapture and Tribulation times will be very chaotic, so something with a battery backup may be a good idea.
This should only be needed for a short time assuming you've made other arrangements for them through a sitter or friends.
Clean Water
This can be an automatic watering system, or something as simple as leaving a sink or the bathtub water running.
Permanent Care
Pet sitters are a temporary arrangement at best. You should arrange with as many of your friends as you can to have them adopt your pets when you are taken. You should agree to take theirs if they are taken up and you are not, just in case.
Contacting Friends and/or Sitters
You'll need some way to let people know you are no longer around. Presumably, everyone will know that the Rapture has occurred, but just in case, here is a site that should help.
http://www.raptureletters.com/
"Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord"