I generally at minimum on trips bring a cleaning sponge, spare eye putty, restringing supplies, and toothbrushes/wig brushes.
My restringing supplies are a head hook, forceps, shoe laces, a piece of wire (the fluffy tube cleaner ones), a long stick with a loop, several pieces of wire, spare head shooks, and numerous pieces of extra elastic. I usually when I restring someone's doll and replace the elastic, I'll keep it and give them the new one. Occasionally it'll work better in another doll and in emergencies, it's better then nothing.
As low temp glue guns are pretty small and have had more then a few times I have wished to have had one, I'd bring this on a crafting meet. I've not used a lighter, but I can't imagine it being easier then using a low temp hot glue gun.
Pretty good list.