Shmoo is completely correct. I just want to emphasize one thing.
If you call
DCL directly, to get the "real" answer, they will only give you the "official" answer of 11:00 and 1:00, they won't even admit that earlier is possible, let alone likely.
When we were preparing our trip with my sister's family, she called DCL and was told 1:00, etc. and I almost couldn't convince her that we could and should arrive earlier and we would get on earlier. Lucky for us, that I read these boards! We took 11:00 PAT's and were on the ship by about 12.
They just tell you 1:00 in case things are running behind; they don't want you to be disappointed. Indeed the day we were there, the Carnival ship docked next to us arrived late and there was a huge line for them. I doubt any of them got on before 1:00 that day. But that is not typical.