My son sits at a special table. He can't eat anything that is brought in by another child. That said, here are some things that are pre-packaged and are safe:
Pop tarts (check the ingredients). We can eat the cherry, blueberry and brown sugar ones in our house.
Freetos and barbque freetos are both safe.
If the child can have milk (mine can't), pudding is a good safe food. Make sure no one else has a milk allergy, they're common.
Several candies are safe. Dum dums, smarties and skittles are all candy we can eat. We can't eat gummy bears, but the child in your school probably can. Jello molds are a good idea (again, not all food allergic kids can eat gelatin products, but an egg/peanut allergic child should be able to).
Most importantly, clean your kitchen VERY WELL if you are making it at home. Make sure you don't inadvertently cross-contaminate. Kids with food allergies are used to not being allowed to eat what the other kids eat. It's really hard on them (my son can not eat any cupcakes, cookies, ice cream, etc...) but they get used to being different. As the parent of a food allergic child, I always send in safe alternatives myself so that other parents don't have to try to figure out what's safe.
Read all the packaging, don't trust anyone else to do it for you. Packaging can change from week to week. Both peanuts and eggs are on the "big 8" list. Both must be displayed CLEARLY on the packaging of any product.
Good luck! Thanks for caring.