You may be able to board as early as 11:00 am. As stated earlier, it depends how quick of a turn around they are able to do from the previous sailing. I was on board the Majesty for my cruise around 11:00 am or so back in the beginning of October, even though my documents stated that the boarding time was 2:00 pm. However, if you do board before 1:00 pm, your staterooms won't be ready before that, but you can go up to the Windjammer to have lunch and/or relax by the pool until that time.
Try not to cut it too close. That was why I was on board as early as I was. With the timing of the flights from where I was coming from, there was a flight that got in at 10:00 am and a flight that got in at 3:15 pm, and figured the 3:15 pm flight was cutting it way too close for a 5 pm sailing, even though the Miami airport is only about 15-20 minutes from the Port of Miami.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)