That is a really hard question to answer. There could be circumstances where the ship might not arrive at 8:00 or where you might not be able to disembark at a specific time. Everything is relative to what happens on that particular day. We have seen people miss their flights because our ship ran into some bad weather and was late getting into the port. I would probably book the latest flight available for that day...but I am not much of a risk taker. Sometimes it is not the distance between two points but what happens in between. I do believe if you book your flight thru NCL, they guarantee you will make it to your flight. Hope this helps some. Perhpas someone who has actually done this will answer.
If the ship docks at 8, trying to make an 11:00 flight is cutting it pretty close--as pata says, there are too many variables. It is probably a 30 to 45 minute trip to the airport if things go well. I would take a later flight. Besides, New Orleans is a great place to explore & the port is quite close to the Quarter--take some time & have a muffalata!
We were on the NCL Dream out of New Orleans in Nov.2004. I also had a noon flight and made the mistake of buying transfers from the cruiseline. This port is very chaotic, and even though you buy transfers from them, everyone gets on the same buses. It was really disorganized with people pushing and shoving to get on. The cruise staff does not help you either. We very nearly missed our flight. What I would suggest to you is that you go to the pursers desk the day before disembarkment, tell them you have an early flight and make sure they give you the luggage tags that put you in the first group to leave the ship. Once you have your luggage and get through customs, just take a taxi. The transfers were not worth it, and only a few dollars cheaper than a cab. Also, it is quite a ride to the airport, so for the peace of mind and less hassle, you ride by yourself and go directly to your airline. Good luck and I hope this helps.
You also have the option of taking your own luggage off the ship with you as you leave. I believe this was called "Express" or something of that nature. We try to travel light so used this method last sail and did get off a bit earlier and faster.
I have heard that Carnival lets you keep your luggage and take it off yourself, but I don't know if any of the other cruise lines do. I wasn't aware of that on Norwegian and I think that's the cruiseline they were asking about. It would depend how much you were carrying also, as I'm not sure how available elevators would be on debarking day.
We did the "Express" on both sails on the NCL Sea out of Houston. The first time was a total nightmare with people stepping all over each other and tempers rising. The next cruise was a total dream, well oraganized and no problems getting your luggage off the ship.