I have done this on our last two trips and I am bringing another suitcase full of food for our trip in December. No problem w/ the airlines and after the food is gone, you have an empty suitcase to bring back your souveniers or to put inside your other suitcase and bring it home.
Just be sure that you realistically bring the foods you'll eat and not too much. And you may really have to force yourself to eat these foods from home when you see those mickey ice cream bars.
Here's an example of what we bring:
juice boxes, small boxes of cereal and plastic bowls, poptarts, granola bars, fruitsnacks, oatmeal, handi-snacks, suckers, ring pops, campbells soup to go (microwave in the food courts), micro popcorn, licorice, pasta anytime, entemens mini muffins/donut balls. fruit cups, raisins, dry snacks (teddy grahams). If you rent a towncar, you can usually request a grocery stop and pick up fruit and pop/water to save you $$. You may want to rent a frigde at your resort ($10/nite at disney resorts) or bring a soft sided cooler.
The food courts at Disney have forks, spoons and knives as well as napkins, and misc. condiments like jelly, mayo, peanut butter etc. Some people use these for sandwich fixins or to make PB and J sand with. This can be a hot topic as some people consider it stealing unless you actually buy food at the food court. I personally feel that it is your chioce but just wanted to let you know it is there if you need it.
Also we would stop at the gift shop in the AM and get a box of donut balls and a qt. of juice or milk for under $6 for all 5 of us. Don't count on getting anything cheap in the parks for breakfast- it will be as much or more that at the hotel.