I think its usually 1:30. Its sometimes available earlier, if you are walking by you can check. Honestly, by the time you board, eat lunch, get any ressies, get the kids to the kids club, and spend a few minutes oohing and ahhing over the ship, its 1:30 and you can drop off your bags.
But do pack light, or a roller. And pack FEW bags - one per adult if possible - or less!. You want to keep your valuables (including electronics) with you - which is why its even more important that you learn from my mistake and not carry on the entire circulating library from your city, plus enough stuff to keep the kids happy for a week, food to last if you get stranded on a deserted isle, a complete change of clothes for everyone, plus swimsuits, etc.
Doing it again, I'd carry:
Documents
Passporter
A little cash (once you are on the ship, you won't need it except for tips - but you'll need to tip the luggage handlers, the taxi (if applicable) and there is a cafe at the terminal which doesn't seem to be open much, but just in case.
The portable DVD player (not to watch, just because it shouldn't be checked).
Enough filling snacks that no one starves waiting for the gate to open (i.e. four cliff bars and two bottles of water).
Camera
Medication (we didn't have any, but if you do, carry it).
I wouldn't have:
books (never had time to read them the first day), except, perhaps, the passporter, and only if it were my first cruise.
A swimsuit for the adults
Swimsuit for the kids (have them wear theirs under their clothes to board.)
A change of clothes for dinner "just in case the luggage doesn't arrive" If I eat in shorts the first night because
DCL doesn't have their act together, tough cookies.
(BTW, most of our luggage had arrived by 1:30-2:00)
One other thing you'll need to carry on, if you want, is any bring along beverages. They do get heavy (one of the reasons I'll just buy my rum drinks on board). But if you require a specific soda DCL doesn't have (Diet Dr. Pepper?) or are bringing booze, you'll need to carry it.
