I-10 thru LA is OK, although I would dump onto I-12 once you get to Baton Rouge to avoid construction delays in Baton Rouge as well as New Orleans area traffic in general.
Haven't heard anything negative lately about I-10 thru MS & AL. I do believe the bridge in Pensacola still has some construction restrictions, but if you avoid rush hour, you should be fine.
Try checking the Dept. of Transportation websites for updates just to be certain.