Check your car numberplate on www.moi.gov.qa to see what type of violation it is, because if it was speeding or red light (unlikely for 300qr) they take a picture of the car and you can ask for the picture as proof of the violation, and this will prove whether it was your car or not.

It's not really enough proof to show them your passport because they don't know if somebody else was driving the car or not.