Simple, just go to the traffic office ( i reckon near Madinat Khalifa)there are a ot of small offices in the premises, you will find Sudanese men offering to do Arabic typing for you. they could charge you between 10- 50 QR to do the whole thing while you wait.
You will need

1) copy of your Dubai licence and original
2) copy of your Qatar ID and original
3) Copy of your visa - just as aprecaution
4) Aletter from your sponsor( sic! I know)stating he/she doesnt have any problems in you getting a driving licence
5) 200 QR towards the fee.
6) 2/3 photographs

You will have to get an eye test done, there is a facility within the traffic department - the sudani man will help you out will all of this.

Trust this helps.