St. Louis is roughly half way between Indianapolis and Kansas City, has plenty to offer, and so makes a perfect overnight stopping point. You can also keep your daughter from getting restless in the car by stopping every couple of hours (or even more often) at state and local parks near I-70, the direct route between your starting point and destination. Besides the Arch, your daughter might enjoy either the St. Louis Zoo or Grant's Farm.
For an alternative route home, take a look at using I-35 up to US-36 east through Missouri to Hannibal, and after that, I-72 to Champaign/Urbana and I-74 the rest of the way to Indianapolis.
AZBuck