Carnival does cruise out of New Orleans, but I think it's a seven day Caribbean itinerary.
How old are your children? Carnival has a very good youth program for kids two years and older. My daughter really enjoyed the activities and the ship's family friendly facilities. I liked the family activities they offered such as family arts and crafts night, name that tune, etc.
Perhaps your local travel agent can help you with the details of sailing out of New Orleans on Carnival.
Feel free to ask me any other questions concerning cruising with kids.
Luisa Frey Gaynor
Family Cruise Editor