My first rifle was a Henry .22 lever action. I probably got it when I was 6 or so. They make a youth version that is a little smaller, and both are lighter than the golden boy.
Single shot is probably a little bit more appropriate, but if she is pretty comfortable with how to use a henry golden boy, consider a Henry .22 lever youth as it would probably be a lot easier for her to shoot. Smaller, lighter by 2.5lbs.
I still have that Henry after 15 years, and it has seen a lot of use.