Do it! I live about 20min south of Fort Worth! We drove it just this past Dec/Jan! (family of 5- three kids aged 8, 5, and 2)
It only took us about 20hrs (actually just under that) using the mapquest directions even with frequent stops for diaper changes, eating, potty breaks for the 5yr old that can't hold it very long (LOL), etc. Mapquest says 20hrs- but if you drive the speed limit -even with stops it takes about that much time.
We did not stop on the way although stopping is not a bad idea if you stop somewhere you would enjoy. I'm just not of the mind to stop JUST to sleep in a hotel and take off again because I'm a night person- so we just switched driving back and forth with me driving at night and everyone else sleeping when I drove (me napping when I wasn't driving in the daylight hours)
If you have a driver to switch with and one of you doesn't mind driving night hours (ie: either used to staying up really late or gets lots of rest to prepare for it so they aren't trying to doze while driving all night!!! or making sure to sleep while the other one is driving) you should be fine driving nonstop. If we can do it with our 3 youngun's... anyone can. LOL