I think its possible, if u get nikah here in qatar the visa is transferable ..

and think this visa is convertable as well, because u came on visit visa from your brother sponsorship ...

u can extend ur visa, and get single exit  entry ..

thne u come back after gettgin married show the nikah to immigration and ur husband can transfer u on her visa...

but im not sure, i will confirm this further .. and come back to you ..

goodluck .. keep digging the information, no need to wait 90 days .. no logic in this ...