You should have plenty of time to get on the ship. The airport is only about 10 minute cab ride to the port. On our first cruise we arrived about the same time and were on board and in our room by 3:30. The only problem is that you are tired from flying and rushing that day. We now take at least one day to stay before the ship leaves. We are refreshed and are able to get on board at noon time and enjoy the day before departure.
We are leaving on the Sea Princess next week and are going 2 days before the cruise just to relax and get some heat. It is 25 below in NY with the wind chill.
Sea Princess 03/01
Golden Princess 10/01
Sun Princess 03/02
Sea Princess 03/03 (back to back)