We drive from Tulsa, OK (not Texas, but close enough!), and it usually takes us 17 to 18 hours to get there. I definitely agree with the other posters, do most of your driving the first day, so the second day is shorter. Our last trip, we made it to Hattiesburg, MS on the first day, and arrived at WDW by 3:00 the next day. You're fortunate because you are in such close proximity to I-10, so you probably can make it to Fla. the first day, which will really shorten your second day. We don't have the luxury of being able to stay on major interstates the whole way, and that's what slows us down. As for your DD, I agree that a DVD or VCR player is a must! My DD was 5 the first time and 6 the second time we drove, and the videos were a lifesaver! If you haven't yet, order a Disney vacation planning video for her to watch on the way. My DD watched hers over and over again on our trips. Also, make sure she understands that it will take two days to get there, and that when you're done driving on the first day, you won't be there yet. My DD was so excited on our first trip that after only an hour and a half she was asking, "Are we almost there? When will we be there?". So, the morning of our second trip, I sat her down and reminded her (at great length!) that we wouldn't be there until the next day. Also, since she always wanted to know where we were, we gave her a map with our stopping point and WDW marked, so we could point out where we were, and she could see how much farther we had to go.
Hope this helps!