By means of AAA maps and Mapquest and other devices, I learned that taking I-10 from La Quinta, CA, to the Houston area is about 1,500 miles, so three days of driving approximately 500 miles each day is perfect. That's about like driving a bit farther than Los Angeles to San Francisco. Not bad.
Taking along a cat, however, is the big unknown. Everything else I can plan for and envision, but how Indy will do ... anyone's guess!