I personally wouldn't do it unless I had enough time to take the backroads and limit the drive to 300-400 miles a day. Driving a Cobra on the interstate is NO FUN. It's loud, hot, windy, wet (on that long a trip you WILL get rained on), beats you up, and you're the smallest thing on the road. The first time passing a semi is an experience.
If you do it, bring raincoats, earplugs, and sunscreen. Consider the size of the trunk of the car you're buying also. Most Cobras are pretty limited on luggage space, but there are some that you won't fit much more than a lunchbox in the trunk.
Important safety tip: If wearing a t-shirt, put sunscreen on before putting on your shirt. If you put in on after putting on your shirt, when your shirt sleeve blows up your arm when you rest it on the door, the part of you arm where you didn't get the sunscreen on will get burned to a crisp and you're wife won't let you forget how dumb that was for a least a couple weeks. ...at least that's what I've heard...