You can get Qatari license if you present the UAE one but:
1. They will retain your UAE license
2. The Qatari license will be valid as long as your visa is valid. Ex.: If you have tourist visa for one month the license will be valid for one month and then you need to renew. When you will have ID they will make the license for 5 years.
This is what I know. The best thing for you is to go to the traffic department in Madinat Khalifa and ask.