Bottom line: not enough info here - of course you can sue - was there a traffic accident report done? I would recommend having an attorney (personal injury attorney who specializes in auto accident cases) look at your case.
Wait------her dad (the owner) apparently has insurance - as an owner he would have liability up to $15,000 - so I would do anything until such time that the other party does something. If they contact her I would submit anything to her father's (owner of vehicle) carrier.
Generally - he is at fault - the vehicle code section is Vehicle Code section 22350 which provides:
No person shall drive a vehicle upon a highway at a speed greater than is reasonable or prudent having due regard for weather, visibility, the traffic on, and the surface and width of, the highway, and in no event at a speed which endangers the safety of persons or property.
My advice? Get an attorney to help out!