I think they started processing us at noon and we were boarding by 12:30 or so. I'm sure it depends on how fast they disembark the previous cruise, but I know we were having lunch by 1PM..
We we went on the Victory (Miami), we waited until about 1PM to get to the terminal and we ended up standing outside for in a very long line.
In Galveston, the cruise terminal is big enough that you can be inside (out of the elements) while waiting.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013