Normally to rent here in Doha, you are required to have certain documents to provide the Landlord with security:

These are normally: RP (not always though as I didn't have one) Employer sponsorship letter (confirming that you are actually employed with salary noted) and post dated cheques against a tenancy agreement.

I know of no where in Qatar that you can rent on a short term agreement without the above documents.

You may be best to hunt for someone who is willing to provide accommodation for a fixed price, rather than going down the tenancy route.