I dont know how you feel about the whole situation, but I do have a 3 year old daughter and if that had happened to my daughter I would be extremely upset. It is the babysitters fault. It seems that you want to excuse the babysitter of her liability and she is fully responsible. I would suggest that you start looking for another babysitter. If it happened to your son, it could happen to any other kid in the daycare and she is totally responsible. Your son and the other kids were under her supervision when this happend. Is your child even going to want to go back to that babysitter after what happened? He is probably traumatized and if he needs plastic surgery it is probably major. You wouldnt necessarily need to sue her but you need to let her know that you expect her to pay for the medical bills. There will be more bills when you are done with his surgery. In cases like this, if she has homeowners insurance, the insurance will cover all the costs for this. She needs to report this to her homeowners insurance and they need to contact you to pay for the damages. You would still need to pay for the daycare since you have a contract with her. Keep all the bills and log all the doctor fee visits, mileage etc, because all of it needs to be refunded to you. You seem to be a nice person and you are trying to be considerate of the babysitter, but what happened to your son can happen again to any other kid in the daycare, i think other parents need to know as well. You should also report it to the daycare association if she is a registered or licensed daycare.
I hope everything turns out ok.
Let us know how your son is doing :(