Sarah, I know where we are staying (Grand Aquarium) there is a 24hour supermarket nearby, not sure where you are staying but as Scunny Jim says, I'm sure there'll be one near you. I'm also going S/C and although we'll arrive at our apartment early morning I always take a few essentials i.e. coffe, tea bags, bread - you can probably buy these at the airport from the shops (although I'm not sure what the shops are like in Dalaman).
Either way, enjoy your holiday