I don't think you are being over protective at all those cutters are scarey sharp and can do long term nerve damage depending on the severity of the cut.
That being said you know your gd better than us. I have a 17 yr old I wouldn't let near a rotary cutter because to him everything is a game, but my 12 yr. old I would let use the cutter because she is cautious and careful, and she understands its not a toy.
Now, if it were me I would do the cutting just for the fact that is she gets the measuring and cutting wrong it might discourage her from finishing the quilt. My cutting is horrible as a result there were 2 yrs between my first and second quilt. If you cut them straight for her she will be happier with her end product.
I cannot wait to see her quilt have fun passing on a tradition. :)