I think that would be Kingsford Smith Drive. Southern Cross Way goes north between Eagle Farm and Nudgee.
The Doomben train does run on Saturdays, but not on Sundays.
There is a 303 bus on week days which will take you from Doomben station, via Portside, almost to the cruise terminal gates, but it only runs before 8:00am. Unfortunately, there is no way to walk into the cruise terminal.