My first sewing lesson was two months past my third birthday while my mother was in the hospital having my baby brother and my grandmother showed me how to sew to keep me entertained. I remember sitting on the floor at her feet sewing up the sides of a very simple jacket for one of my dolls. It wasn't too much later that I "sewed" by sitting on her lap at the treadle machine while she helped me guide the fabric. She did do the fabric cutting for a short time but I was making simple doll clothes completely by myself by the time I started school.
I don't remember ever poking myself badly with the needle or pins, but as others mentioned, you could start with mesh and yarn with a blunt needle until she gets the hang of it.