She's 100% at fault unless:
- you hit her square in the rear, and
- you were travelling too fast for the conditions.
Most rear end accidents are 100% of the person that runs into the car, with the exception if the car infront pulled a manoeuvre that didn't reasonably leave you enough time to stop. Even if she pulls out infront of you, there is an expectation that you had time to slow down to avoid hitting her - so I hope you weren't speeding. Be very clear about how little stopping distance she left you.
If that is true, you did the right thing hitting her. If you pulled out and hit a car head on, it becomes 100% your fault, even if you were trying to avoid an accident.
