RFID for proximity on/off - small reader

I am looking for any suggestions on how I can make a very small RFID switch system that is ON when the RFID chip is not nearby and then shuts off when the RFID is close by. They will be within 4 inches or so. I want my cat or dog to have the RFID chip on their collar, and then have the on/off reader in a small package, as small as possible. Can anyone point me in the right direction?