According to Disney's top executive, Disney Cruise Line's ships are already three quarters booked for this year.

"I think that says a lot about the business and the economy," Disney President and Chief Executive Officer Bob Iger said during an interview with CNBC shortly after Disney reported its fiscal first-quarter earnings. "Generally speaking, we're looking at a very, very healthy year ahead for that business."

Still, Iger acknowledged that Disney Cruise Line bookings slipped in the aftermath of Carnival Corp.'s Costa Concordia tragedy recently off the coast of Italy.

"The entire cruise business was affected by the crash in Italy. … Our call centers have decreased in volume, and our bookings for the week were down somewhat because of that," Iger said.