Is Benadryl an antihistamine?  Cause I would be packing one, as well as panadol.  We keep bandaids, burn cream, aloe vera gel, paw paw cream (for mild burns, rashes, bites etc...), bandages, sling & cotton wool.  I do have a proper first aid kit I bought and that it is in the bathroom, with a first aid book and a list of emergency numbers - just in case!  I'll ask my sil what she carries as my niece sounds like your daughter - severe allergies and an epipen that goes everywhere.

Dont forget to include her Dr.'s phone number and any other emergency numbers and her medical number or insurance card on a card that can be attached.

I would also include a water bottle unopenedand and at a camping store find a thermal sheet. It is a silver plastic looking blanket but is thin and in a package but keeps people warm that may be in shock.

I would of course suggest that you also make the whole family first aid kits and make several. One for a travel bag and one in each vehicle.

I would include a brief, but accurate, description of what her allergies are and what someone should do in case of emergency. 

I was gonna say an instruction sheet, for if she has a reaction and you are not there and someone else has to handle it. Not everyone is conversant on the use of an epipen. And an action plan: If she has contact with...then this is what would usually happen...this is what you should do. Do this for each of the allergies.

I'd write a list of allergies and emergency contacts, etc, and tape it to the inside lid of the box! Just in case something happens and someone else has to take care of her.

Other than that, I'd put some alchohol swabs, some gauze, tweezers, a thin maxi pad (cuz they are really absorbant, and sterile, for bad cuts and the like).

Sorry no suggestions for the food allergy part.