You should have multiple back up sitters available in case your primary sitter is taken up in the Rapture
For advice on picking a pet sitter, check out Evaluation
You'll need some kind of auto food dispenser. The Rapture and Tribulation times will be very chaotic, so something with a battery backup would be a good idea. Check out Products
This should only be needed for a short time, assuming you've made other arrangements for them through a sitter or friends
This can be an automatic watering system, or something as simple as leaving a sink or bathtub water running
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 pet 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, every will know that the Rapture has occurred, but just in case, here is a site that should help.