Her insurance covers her for driving my car but will my insurance company be notified?
Speeding tickets go with the driver, not the car. As for the no insurance in the car at the time of the stop (that is what your saying right?). If so, if there was insurance on the car but you just did not have the papers, give the information to the court proving it and the ticket will likely be dropped relating to the insurance.
I am an Arizona attorney. AVVO does not pay us for our responses. Simply because I responded to your question does not mean I am your attorney. In Arizona a non-lawyer is held to the same standards as an attorney so there are dangers to representing yourself. This is for informational purposes only and should not be considered as legal advice. If you require legal assistance an in depth discussion of your case is needed as there are many other issues to consider such as defenses, statute of limitations, etc.