After getting hitched in Arkansas last month, the 19 Kids and Counting stars retreated to the beachside town, where they rented a house.
"Every morning, we would wake up and go out and sit on the deck and listen to the waves," Jill, 23, told People. "It was beautiful. It was very private without a lot of people there yet for the season. It was so relaxing."
Duggar and Dillard, who kissed for the first time on their wedding day, snapped selfies together on the beach.
"Celebrating our weekiversary!" they wrote.
The happy couple, who stuck to the Duggar family's conservative courtship traditions, became engaged last April. Jill and Derick first communicated online, while he was doing mission work in Nepal.