I'll be sailing on the same week on a different cruise line to the Western Caribbean, maybe will run across one another ashore.
The Norwegian Sun is a beautiful ship which is maintained very well. I recently sailed on her in December 2005. You're going to have a great cruise.
NCL has express disembarkation along with the normal disembarkation. Express disembarkation isn't effortless while normal disembarkation is. With express disembarkation, you carry all your bags, so pack light. With normal disembarkation, you place your packed bags outside your cabin door the night before, and the crew move your bags ashore, where you pick up your bags. When you depart the ship depends on the color tags you attach to your bags.
When's your flight? You can reach Miami International Airport easily within an hour off disembarking the ship if you use a taxi cab. You should also reserve an hour to get through security at the airport and to get to your flight's gate. It might take longer if many other cruise ships return to Maimi the same day.
But here's a rub, since you are not a native citizen of America, you'll have to meet at a public room aboard the ship to pick up your passports. I'm not so sure you'll be able to use express disembarkation. It will be important for you to inform the appropriate personel when you flight takes off so you'll get the appropriate color tag.
P.S. Here are two links to photos I took on my last cruise aboard the Norwegian Sun.