I put together a small first aid kit for my 8 year old daughter's pack. It consisted of a red altoids tin, 3-4 band aids, tweezers, nail clippers and an emery board. Not much, but it gives her a sense of self sufficiency.
I recently found a small waterproof container for a buck at Goodwill that I'd been eyeing on eBay.
Since it's bigger than the tin, I've decided to combine her kit with a few emergency fire starting tools like vaseline covered cotton balls and 2-3 matches. Again, it's not much, but if I want her to be responsible, she has to be knowledgeable. I can't expect her to respect something she has no experience with, so next time out I'm helping her make the first fire. I figure, worst case scenario, that's a skill she'll need.