I have seen females riding .

There is no specific license for sport bikes. Just get driving license for motorbikes , in general , you can ride whatever you want ( cruiser, sport, adventure , etc. )

To get it , go to any of these driving school ( Al Khebra , Doha modern drving school , Al Raya , don't remeber the rest )
It's 15 days course , you can take test in between if you are ready.