Hi Amy:
I spoke with a moms panel foodie expert,
Erin F., for some insight.
First, the quickest way to get from Magic Kingdom to
Fulton's Crab House for lunch at Downtown Disney would be to take the walkway or monorail to the Contemporary Resort (about 10 minutes from Magic Kingdom) and hop on a Disney bus to Downtown Disney from the Contemporary.
Other seafood-based restaurants open for lunch are
Coral Reef at Epcot (you will need a
park hopper option on your tickets to visit more than one theme park in one day) or
Shutters at the Caribbean Beach Resort.
To get to Epcot from the Magic Kingdom, take the monorail to the Ticket and Transportation Center and then transfer to the Epcot monorail. To get to the Caribbean Beach Resort from the Magic Kingdom, hop on a Disney bus outside the Magic Kingdom to Caribbean Beach Resort.
Enjoy.