I have done this at a few places.
1. Beaches & Cream.
2. Brown Derby (though it was just an appetizer and grapefruit cake)
3. Whispering Canyon.
I would say that Hotels would be more likely to accomodate you, than park places, but to be honest, in my opinion, much of the "out of park" food is better tasting, but it is worth it to eat "in park" for the experiences that each place can give.
If you are off site, it is likely that your food will be cold by the time that you get back, unless you are in the Downtown Disney areas.
If that is the case, you will have a plethora of great places that you can get takeout from!
-What resort/hotel are you staying at?
Maybe a local can tell you a great place near your "home base".
Hi we are going to be there Dec1-10th I have made about 7 ADRS already for varius times and dates. We are travelling with our 2 1/2 yr old son and sometimes he is too tired to sit through a complete dinner with us. Do you think as there are some special places for dinner and desert we would like, could you go to the podium or call ahead and order the meals and desserts take out to enjoy back at our room with our cranky/sleepy toddler? We do this a lot at home as it saves aggrevation for all concerned, but can you do this at Disney? This year we are off property as well so no room service available to us. Just thought I would ask before we get there. Thank you for your help 
Conor's Mom
