You have to go to the Police station at Madina Khalifa or enquire them by giving a call, they will clarify your stance that your Bahraini License can be converted to Qatari License or not?

I had a Dubai License and they converted mine License to Qatari License.

For Obtaining the Qatari License you first have to get your visa proceedings completed,and get your RP and Qatari ID.