Hi Sandy,
as everything here is strict, driving any vehicle is very difficult as well. You should only drive if u have got a Driving License. Moreover, if u are a foreigner and u have done an accident, u will be immidiately deported back to your country instead of giving u a fine slip. It has happened in the past. My cousin's friend got deported beccause of this law. So, please be careful and better take a taxi instead of taking any risk.
Doha is a safe place to be (with regards to security) for the exception of their driving which is indescribable. My first impression when first driving there was:' have I got myself into a racetrack by mistake or what?” Some really drive as if they're in a big hurry to get themselves killed and mostly without noticing others (whether in a car or a pedestrian) so be VERY CAREFUL!