It depends. As already noted, you can check your bags and get boarding passes at your resort if you are flying out on a participating airline. BUT...if you have carryon bags, you will need to stow them someplace. So, that means either at the resort or at the park. If at the park, it will cost you, and you may need more than one locker if there are multiple bags. But, that would enable you to get a cab directly from the park. So, you could head out of the park by 10:30ish.
If you don't do that, and you leave your carryon bags at the resort, you will have to be back at the resort by 9:30am. DME will give you a pickup time of around 10am for a 1pm flight. You need to be back at the resort with plenty of time to get your carryons out of storage and then be at the DME bus stop 15 mins prior to the pickup time.
With a 1pm flight, I'm just not all the sure you have a lot of time to spend in a park..unless you are able to walk to and from the park. Otherwise, you need to figure on at least 45 mins to get back to your resort from the park, using Disney transportation..including any waits.