Ahoy, Theresa!
It's been a few years since we've had our passports stamped in Nassau, but when we did it was quite simple. When you exit the cruise ship, go to the end of the dock and turn right. You'll see a tall, skinny yellow building, which houses the immigration office. Simply tell the guard at the front that you'd like to have your passport stamped, and you should be able to enter. Follow the directions to the Immigration Office, and the Immigration Officer on duty should be able to help you fulfill your request for a passport stamp!
The process may have changed since our last visit, so I encourage you to visit the Port Adventures Desk onboard and check in with a member of the Port Adventures team before your stop in Nassau to get any updated information about passport stamps.
Please use care and caution when carrying your passports off the ship. Make sure to keep them dry, protected, and in an interior zippered pocket to protect them from theft (Disney Cruise Line recommends leaving passports, air transportation tickets and other travel documents in your room safe). When going ashore, adults are required to carry their Key To The World Card, a Driver's license, and a copy of their passport or other government-issued photo ID.
I hope this helps with your planning. Enjoy your magical voyage on the beautiful
Disney Dream!
-Diane W.