I would like to know if there is a way to determine a girls pitching speed without a radar gun?
Video camera, count the frames, apply the frame rate to get the time, convert to velocity. Using higher frame rates result in more accurate readings. If you're throwing at 43' and 30FPS I can save you the calc, 15 frames is just under 60MPH from 43', 14 frames is just over 60MPH. Don't even worry about it until she's throwing it in 15 frames.
Of course if you don't have a video camera, a radar gun is cheaper.