If you have a small point and shoot that also does video (which most do nowadays) just get a suction cup mount. I've done this repeatedly with great results, the gopro is a nice unit but single purpose really, and unnecessary IMHO. I haven't done a car video yet, but the snowmobile video below was done with a small Nikon point and shoot and a suction cup mount that screws into the 1/4" standard tripod fitting on all cameras.
Art