you are in a grave situation here. since  your wife is out of Qatar, you do not have her passport. more over im sure even if she couriers you her passport you will not be able to extend her visa.

unfortunately i think you will have to reapply with all the documents.

you can give one try by checking with the immigration if your wife can courier her Passport to you and if you can extend it.

You may also want to check with the Qatar Embassy in India. Im sure they can help you renew the RP

hope that helps.