Actually, they leave pretty early. I had a choice between an 8 something arrival and a 12:45 pm arrival....Disney told me that 12:45 was too late!
You will be met by a Disney agent at the airport and escorted to the bus. As soon as a bus is reasonably full, it will head to the port....usually only a 5-15 minute wait. Disney agents will claim your luggage and get it on an appropriate truck to the port (it usually doesn't go on the same vehicle that you use!) That way, you don't have to wait for luggage claim or anything.
You will probably arrive at the port about 10. There is a snack shop there, characters come out, etc. If you want, you'll have time for breakfast at the airport before you hook up with the Disney people.
When you get to the port, the adults need to get in line to register. My teen gets in the boarding line, and I join her after I've done the "document drill." When she was younger, she'd hang around with the characters, check out the model of the ship, etc. They don't allow private cars into the port till about 10:30, but the
DCL busses get in "whenever."
