I think I would make it worth her while to slow down. If she's old enough to use a sewing machine, she's old enough to learn how to use it responsibly. Either she can start doing things to earn money to pay for the new needles, or once the needle breaks, she can't sew for a couple of weeks because you have to wait for payday (or some similar logic) to buy a new needle.
I think it's sweet that she's sewing with you, but I don't think it's fair that you bear the cost of her recklessness.