I haven't run into any "restaurant" that doesn't accept DDP. Quick service is usually entree and a dessert. You can have a salad or a burger lets say, but you will have to pay for one or the other if they are not listed as a menu item together. I just look at the menu like Caseys Corner says "All hot dogs served with apple slices or fries". Cosmic's says "......... served with apple slices, french fries or cucumber salad"
At lunch anything on BOG menu is included in the QS DDP, but BOG didn't have anything "healthy" as an option. I have seen sliced apples as a healthy dessert at other restaurant so look at the kids menu. That being said I have never seen a menu restriction on an DDP menu. At table services J usually goes with the most expensive steak on the menu and has never been restricted. At Narcoossee's when we order the Lobster dinner we don't get refused. The only time we have ever had a problem on the DDDP is out in DTD we were told that appetizers for two were not included as appetizer.
Look at the kids menu for the healthy desserts, that is usually where they will be listed if not listed a in the description like above.
One thing to remember on the QS DP is not limit yourself to burgers, chicken fingers, and hot dogs every meal, mix it up and enjoy.