Sorry, I TOTALLY DISAGREE - if you get there early there is a very good chance you will get caught up in a big crowd just waiting for the boarding pass processors to open up. Then you wait in line to get processed and then you wait in line to get on the ship then you wait in line to get your picture taken.
Some people MAY get there at 10:00 and be lucky enough to get on if the ticket booths are open, but often they are not open and the big rush happens very soon - at 11:00. Then just getting past the photographers and into the ship can take 90 minutes.
The BEST time is about 3:00, you will walk straight up to check in and directly onto the ship.
Everything on the ship is closed until 1:00 pm (except the buffet) anyway - you can't get in your cabin. You end up having to carry your carryon bags around the ship and fighting crowds in the buffet. Then at 1:00 you get in your room but your luggage isn't there yet.
Go later for assured easy access. BTW: this is ESPECIALLY true for big ships 3000 passengers+