You dont need to waste an Arduino on a dumb ON/OFF wireless sensor, see
http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1293839127
Dumb Dirt Cheeep Wireless Environment Sensor
Use the first example, and have the door switch in series with battery.
The TX is less than $1 of parts plus your module. For longest battery life, have the TX turned off in the state the door spends most of its time.