.. at your countries embassy/consulate in qatar. Or the nearest which may be in Dubai. If not you would have to make a trip to your home country. And whatever you do, try to do while you have 6 months remaining on your passport.

I've renewed my Indian passport twice in other countries and have not had a problem. I have not moved to Qatar yet, so i hope things are not too different there... would love to find out from others staying there