Made that trip this last fall.... down to I-40, you will be fine. However, the road gets real "hilly" from there on south. Personally, I would recommend that you turn east on I-40 to the outskirts of Little Rock and cut down to I-30 west. Once you are back on a westerly track, you will have several options for turning south into Louisiana, depending on what your final destination might be.
John (Rusty) & Jessica + Sarge $ Rufus
2013 Newmar Canyon Star 3953
2014 Honda CRV