Powering My New LED 10-Volt 10-watt R.V. Lights

1) i haven't worked with a 7809 in years but always thought the max current was 1A.
2). I never considered it good practice to build a circuit that pushed the specs beyond about 50% ratings.

Given the recently posted new information I would have to withdraw my previous comment that the 7809 would be a poor choice although I'd probably be inclined to use an LM340k instead.