As of now, no (assuming 12+). You will need to go to the Safe Passage website and upload your vaccine card to the Pre-Sail Screening area. Once they review the card the site will switch to show "Cleared" for all three tests that show (Pre-Sail, Embarkation, Disembarkation).
There IS a mandate for cruises starting or ending in Bahamas to have testing, but if the Bahamas is just a port stop, then you do not. We're on a Dream cruise as well, and just got off another line that stopped in Nassau. No testing needed.