A woman hit the back of my car and blames me! Can she get my details from the number plate?

Without a police report there is no point getting uptight about the incident. If she claims against you after getting your contact details then it is her word against yours. As there was very little damage done she would be daft (under normal cirstances) to make a claim. If, however, she is running a scam she might try to extort money from you privately - by getting threatening official looking letters sent to your address. The best you can do is to notify your insurer all of the information and supply photos (with a date stamp). If this woman then contacts you you can then make a counter claim for harment, fraud or what ever.