Welcome aboard, Erin! How exciting that you're planning a Disney Cruise to the Mediterranean! That is sure to be one very magical sailing!
Dubrovnik looks to be an amazing port to discover, and the Port Adventures offered there are sure to be spectacular! Dubrovnik does not require tendering, so you should be able to walk directly off the ship onto the port dock there. This certainly makes for an easier transition to the port and a faster time disembarking and embarking later in the day.
Take a look at Disney's website with the
12-night Mediterranean cruise itinerary. You'll see that the only ports listed that require tendering on this sailing (noted with a star) are Villefranche, France (Monte Carlo, Cannes, Nice), and also La Spezia, Italy (Florence, Pisa). All of the other stops on this itinerary will pull up to the port dock.
I hope this helps you plan your cruise, Erin! Let me know if I can help you with anything else before you set sail!