I-55 is open southbound through MS so you should be OK, but be advised, fuel is in short supply in MS and LA. I'd highly suggest topping off in Memphis then top off once you get below 3/4 tank until you get to your destination.
If you want to stay on interstate the whole way, your best bet is I-55 all the way to Hammond, LA, then west on I-12 into Baton Rouge (we have fuel but our supply is running short) and then pick up I-10 for the last 60 miles into Lafayette.
If you don't mind secondary roads, I'd suggest I-55 to Jackson, west on I-20 to Monroe, LA, south on US-165 to Alexandria, LA, then south on I-49 to Lafayette. You may fare slightly better going the second route as far as fuel goes, but it will take longer.
Be advised, our security situation is dynamic at this point and is constantly evolving. The closer you get down here, the fewer supplies we have and the more irate the refugees get. I"m expecting looting and rioting within the next few days regardless of SWAT/Natn'l Guard/miltiary presence. If you come, come loaded for bear. Watch your 6 and keep as much fuel in your vehcile as you can afford.