First: A Strong Dose of Reality
Welcome aboard the RoadTrip America Forums!
There is simply no way that you can leave Dallas in the afternoon/evening/night and be in St. Louis for your first night's stay. No Way. That's a drive of over 600 miles. More than professional long-haul drivers are legally permitted to drive in a day due to safety limitations. And far more than you should be contemplating driving in a single day, let alone one that doesn't start until a good chunk (most?) of the day is already gone, let alone with an infant on board. I cannot emphasize enough how bad an idea that is. You should plan to start as early in the morning as you are able. Also plan on making at least a couple of short sanity breaks along the way. And finally plan on getting no farther than halfway to Chicago - roughly Lebanon MO.
AZBuck