Even better idea would be not to go to HIA at all. Just go to Kidzmondo in Mall of Qatar and sit inside the Qatar Airways plane and click photo and come back. Show this photo while making new RP.
Seriously, You need to get exit and entry stamp on your passport. Its not for fun that they make such rules. Since you already have a ticket, why not travel and come back in a day or 2. You have a visa that will be tracked upon your entrance. you need to complete the procedure for that. Go and have fun.