In my experience with Dells in the past, they've just about always used a 19v power supply, and they really don't like running off, say, 16v that a Thinkpad power supply puts out.. So they're definitely not going to want to run off the 13.8-14.5v that the car puts out. It's easier for the electronics to step the voltage DOWN than up.. Hence the 19v power supply with a 14.5v battery, when the computer is running off 5v and below.
I don't know if the plug on this laptop is the same as older Dell laptops, but if it is, any of the readily available Dell car adapters on Ebay will work fine.. I had an Inspiron 1200 that took a plug alot like this one, not totally sure it's the same though. And it put out 19v, and more than enough available amperage. I don't have it anymore though. Loaded OS X onto that Laptop and made a mint on Craigslist..