Since you are asking on behalf of your child, if it will help her feel more comfortable to know that her favorites actually came from home, YES, you can bring cereal and popcorn. As others said, to be safe, don't pack in your carry-on. That might be tragic for your child if she sees her favorites tossed by TSA.

Ling and Sons is a great market. Most things are reasonably priced.

Don't overload on food from home, but again, if it soothes your little one, certainly bring it.