A new Publix opened last year just north of the Orlando Premium Outlets. It's the closest Publix to the Courtyard at DD, and it's a large, well-stocked store.
I would recommend asking the front desk for a map and exact directions.
The directions are basically: (1) Turn right on Hotel Plaza Blvd. (2) Drive toward Crossroads Center (but not into the center). (3) Turn right at 535. (4) Drive under the I-4 freeway and get into the left lane. (5) Turn left on Vineland, which is the first signal after the northbound I-4 onramp. (6) Drive on Vineland for two miles or so. (7) Turn left into the lot when you see the Publix.