My suggestion is to contact shipping / cargo agencies for that. They will guide u perfectly as the rules are different for different countries.

Usually :

1) The car model is very important i.e it must be less than 5 Years old. This rule need to be confirmed by Saudi customs

2) You have to deregistered the car from Qatar and to get export plates

3) Then You can drive through after getting clearence from police

Or

you can contact transportation company to transport ur vehicle to Saudi