Hi there, Kimberly!
Disney's Hilton Head Island Resort is such a departure from a typical
Walt Disney World vacation. The pace is peaceful and laid back, with southern charm and hospitality at every corner.
There is not a character dining experience at the resort, as the small island locale doesn't really have the space for a table service meal. The main "character" experience you may have when you visit is with Shadow, the resort's resident golden retriever. You can find Shadow with her handler, B'lou Crabbe, at various times during your vacation. And if you can't find her in person, there are hints of her throughout the resort, including the adorable golden retriever stuffed animals available at the gift shop.
I have heard of an occasional appearance by Pluto, but there isn't a schedule. You can check with the front desk when you arrive to see if they have anything like that going on during your stay.
Enjoy a magically relaxing vacation, Kimberly!
Anna