The distance is 400 miles approximately. I've driving this route several times and driving time is between 5 and 8 hours, though it depends on how many stops you do and your speed of course. My suggestion is to do the stop over at Lafayette. There are some fantastic restaurants in/near Lafayette serving delicious cajun food.
I would suggest hitting the road as early as possible or avoiding going through Houston unless you can time it to drive thru between 10 a.m. and 3 p.m. You really dont want to find out the hard way by being stuck in traffic jams for hours