getting power from the dome light is a bad idea. the dome circuit in most toyota/lexus is live all the time, except when teh computer decides to turn it off (like if a door was left open or something). so in theory it could kill your battery unless you added a battery drain prevention kit. even then i still wouldn't put it on the dome circuit - if your rx is anything like my wife's highlander, there's a switch in the console for the dome lights that lets you control ALL of them in one place for ON/OFF/DOOR, so if fir example the kids are playing with their dome lights in teh back, you can just turn them all off with one switch. kinda like the window lock button on the driver door.
doesn't your car have a lighter socket in the back that you can tap into? my rav4 and my wife's highlander both have them.
i would also recommend mounting it at the TOP of the glass. yes, it's a bit more work, but it will be worth it in terms of a clean install and better viewing angle. does the back glass open separately from the door like it does on the highlander?
search for my thread on installing the blacksys cf-100 in a toyota sienna - it has photos showing how to run cables through the factory rubber tubing so that you don't have wires hanging loose, and don't have water leaks.
one other possibility that might make it even easier for you since you're in canada, and all your lights are on any time the car is on - tap into the license plate lights inside the back door. that would be simplest, and wouldn't require trying to feed a wire through the rubber tubes. it would also mean they would shut off when you turn off the car as well, so almost no chance of a dead battery because of the camera. there's plenty of room to put the original lighter adapter and a new socket inside the door, just make sure you tape the adapter into the socket so it doesn't vibrate loose over time.
note about the license plate lights though - if they're LEDs, make sure the wire you tap into actually provides 12v. some LEDs run at less than that.