This looks a runaway marriage and how did you people manage to get qatar visa. Marriage is only possible through either one's embassy only and it will take considerable time for processing these documents. A NOC is also needed, however that can be arranged through friends. Nothing like Urgent is possible here as this is a different country for both. Anyway best of luck, but tell me how you both will manage life without the involvement of your families. Do you people earn enough to manage life ? Have some family members or friends to support later on.
Another option is to visit a major city in india and contact awqaf department to assist you in marriage.