There is a very nice kennel 5-10 minutes from the resort, it is called Evergreen Pet Lodge. We have boarded our dogs there several times. It is very clean, with a very friendly staff. It was recommended by
DVC-HH. The phone number is 843-681-8354. They are open every day of the week. They give a discount (15%?) to people staying at DVC-HH.
Not sure when you're going, but at certain times of the year you are allowed to walk dogs (on a lead) on the beach. I know you can do it in the winter. We go and get our dogs from the kennel, take them for a long walk on the beach, then take them back to the doggy "hotel". Fun for everyone!
