You say that the output wattage of your converter for your laptop is 19W. The converter I posted has a maximum wattage rating of 75W. Thus meaning that it will run with no problem. (Not with this specific one, but in the past I have even hooked up a TV and XBOX to one of these).
With these adapters, all you do is plug them into your cigarette lighter (12v outlet.). This will then convert the power from Direct Current(Car) to Alternating Current (like in your home). The front face of the converter will have either one or two outlets that look exactly what comes out of the wall in your home. Just plug in your adapter into the converter and "viola"! You have power.