If it were me and I was in my house, I'd find it much easier to just use a microswitch, some wire, an LED, resistor, and a wall wart. Now, I understand that if your garage is quite a ways from the house, running the wire might be the problem, so this might be why you want to use RF. Even in this case, one other thing to think about would be to add a laser pointer and a photodiode and perhaps a transistor or comparator. You could mount the laser to turn on and shine towards the house when the door is open. Use the photodiode to detect the signal and turn on an LED. Mount things up high so someone doesn't get the laser in their eye. While this is more work, I suspect it would be a tad easier than getting an RF transmitter/receiver setup to work.
