Unless Disney has done away with it, Disney offers their own shuttle from MCO to Port Canaveral. It's pricey, but they'll take you whatever day you wish to go. You may have to go the following day if you wish to spend the whole day at MK. You usually have to be at the port by a certain time (no later than early afternoon IIRC). In the past, you could just bring your luggage down to the lobby of the Hyatt somewhere and they'd put it on the bus for you.
This is separate from DME.
ETA: sorry, I think I misunderstood your OP. It looks like you were asking how to get to and from WDW from MCO, rather than from MCO to the port. While I would still recommend going to the port the day after you go to MK, if you can arrange your schedule that way, I would rent a car at MCO. MCO is probably the easiest airport car rental I've ever done. Most rental agencies are right there without having to take a shuttle. Just rent a car, drive it over to MK for the day, drive back that night. If you've already checked in to the Hyatt for that day, I can confirm they will store your luggage for you if a room is not immediately available.
