My apologies Marle, I did not intend to come across aggressive.
Thank you for your response PE. I don't believe heat should be a concern for this project, as it is just going to be turned on for short periods of time (1min or so) a couple of times per day. As far as the drive voltage, I should have plenty for the drive voltage (9V), and my gate voltage is going to be at 3.3V with a 3.3V Arduino. As you can tell, I have never used a FET before so I thank you for clearing up that. You said that the FDD8447 would work well assuming I had a 5V Arduino, and the minimum gate voltage would be at 2V. I'm assuming this would also work fine with a 3.3V gate voltage, would I run into any issues with that?
So, to clear up any misunderstandings, I am running a 3.3V Arduino with a 950-1050 mA LED. My gate voltage is going to be 3.3V from the arduino, and my drive voltage will be 9V from a battery (not a supply). The LED will be connected to the 9V source.