As mentioned before...go to the Supreme Health centre.

The queues are long so be prepared to wait. If you can register and pay over the internet (Arabic only) it goes slightly quicker (only slightly) - you still have to queue. When I arrived there where 150 people in front of me and it took 4 hours.

Process:
Go to the counter, with passport/Visa and paper (receipt) get a stamp.
Queue for Xray, then Blood, then health check.

Wait 3-4 days for results.

If ok then you need to go to the ministry of interior to get your finger prints.
Again an appointment is required.

Do yourself a favour get a few passport size photos - with a BLUE background (has to be BLUE...) as you need them on virtually every form.

After finger prints wait 2-3 days..Qatar ID and RP is can be collected.

I was lucky my company managed most of the appointments and taking me to the places.

Good luck.