We have driven to WDW from NE Ohio a few times now...always with little kids. Takes about 18 hrs. We always pack a few new travel-toys (cheapy ones), and pull one out whenever the kids get a bit restless. Also, we always plan to stop at rest areas here and there, to run around, throw a frisbee, whatever ... but we never seem to need to actually do it more than once or twice.
We do drive at night, but DH will fall asleep driving so I drive all night long. If my eyes get too tired, I pull into a rest area, park near a security car, and snooze for a little while. On some trips, I have pulled off for a half-hour snooze at EVERY rest area...that was when we drove all day, and planned to arrive in the morning. By 4am, my eyes were DRY!
So this past trip, we left home at 3am or so...and drove through the wee hours, and all day long...stayed at a cheapy Days Inn, arriving around 10pm there. Next time, we will do that again -- leave around 3am again BUT will go to our WDW hotel, even though our arrival will be late because I didn't like having to get up in the morning and drive to the hotel.
Sorry, got wordy. Just wanted to give our scenarios, so you can balance pros and cons. We have never split the drive in half, because I wouldn't want to sit in a car the better part of TWO days in a row!!
How old is your baby? Crawling yet? Walking? Teeny? That will make a difference for you too-- a mobile baby will want to get down and move around once in a while. A Teeny baby will probably do better spending more time in a carseat and sleeping more.