I've done 3 cross country trips in old Mercedes, and I know you don't think so now, but 12,000 miles in a month will NOT be enjoyable. I'm the type of person who can't doze off with the TV on, and certainly never get that feeling behind the wheel. 15 hours of straight driving brought it on for the first time in my life. That was from Costa Mesa, California, to Amarillo, Tx, a bit over 1000 miles in one day. I couldn't get myself up the next day to finish the trip either. I didn't hit the road until noon. You can't expect to have more stamina than professional truck drivers.
I suggest you try and cut that number in half and stop and enjoy yourself. Be sure to take photos. I may only have one or two cross country trips ahead of me before I become a grown up and can't take off for two weeks. At least I'll have the pictures.
Ol' Turbo's cross country trek, to boldly go where...
Ol' Turbo is at it again... Another Cross Country Trek
Second Cross Country Trip: Photos
As long as you have the means financially to handle a major failure along the road, be as prepared as you can for emergency repairs and have fun. If you don't have access to cash just in case, it will be a foolhardy venture. Do not go into this trip with serendipitous expectations despite the car's name.