One trick that worked with my daughter (she is 9) to complete projects was she could pick out more yarn. (perhaps mom should have taken her own advice :roflhard: I would have finished a lot more projects and had way less yarn!)
I have also had her look through my knitting magazines looking for what I find that interests her. Some ideas she came up with were a simple purse, a headband, a triangle shawl (easy pattern that teaches one increase each row.), a skirt, and a hat.
There are several books out there that have fun projects for kids. A couple off the top of my head are both Knit Girrl Books, and the Klutz book in the kit. I did find a couple at my local library that was geared for girls around her age that she liked. She is currently helping me make a her a blanket. (The link is below. We are making it larger than instructed, by adding another color and more squares.)
She mainly knits when I am reading to her and her brother. She can’t knit while waiting movie or the TV like I can. If I need to go the LYS for help (which I find I do less of now that I use the forum!) she takes her project and works on it there. Sometimes she takes in the car with us, but not very often.
I hope that gives you a few ideas, it’s great we can have kids learn early!