Should be, 12V dc is 12V dc... (kind of - neglecting AC ripple) I forget the pin assignments on the computer power connector but its usually pictured on most power supplies... or just use the ol multimeter on a live one... (the connector is intended to carry 12V dc 4A so check the current draw as well...) You should be able to take the power off the cigarette lighter if its not already used for something, either behind it and twist the wiring directly (with small marettes or solder and tape) or using a cigarrete lighter adapter that you can sacrifice.
Does the lamp actually use 12V dc? What is the current draw? Also, add all this kind of stuff up, does the total VA required fall within the capability of your alternator?
You might want to look into the power inverters and solar panels available at Canadian Tire for pretty cheap now...
DISCLAIMER: I'm no expert on this stuff, I just come from a "red-green" type familiy... my buddies refer fondly to my "twisties" for electronics purposes, always with a little disdain...
Also: extreme care should be taken with any internal lighting as it can be a significant safety issue, it is illegal to run with the "dome" light on here... if the mounties are really bored they may stop you for it.