Very Simple
1) get your eyes checked from any eye glasses shop such as Jaber ( they have several shops allaround in Doha - even city center)
2) take the result with your old driving license and go to the Marour ( trafic police ) in Madenat Khalifa apply the papers and get your new DL with in the minute.
Note : you will need to pay a renewel fee ( it was QR 150, now it might be mor) and to pay you must have a Visa card or Visa ellectron- master card , what ever electronic mean to pay...they do not except cash
Best of luck
Think they will open as of Sunday
best of luck