First, did you have any police called during this situation or did you just exchange information/insurance?
Never admit that you are at fault.
Most likely insurance will find you at fault. There are some extremely rare situations where you will not be found at fault though most likely would not be in that situation. Since i'm going to assume you and the affected party is under 18, my own personal opinion is to pay her damages out of pocket as your insurance rates will sky rocket as young teenage drivers are at the "highest risk" thus leading to your insurance sky rocketing. Even if you can prove that she was speeding, she no matter what always has the right of way. Unless you were more than half way out when backing up and she hit you due to not paying attention as you said, then you can easily file a claim for that. I know it feels like it isn't your fault and that you've tried your best in avoiding this situation from happening but unfortunately these things happen frequently that cars being released are slowly being required to have "necessities" like back up cameras/side cameras/ and even turning cameras. Take this as a learning experience to back up extremely slow and to always double. triple check because there are a lot of extremely terrible drivers out there.