I think your indian salary is very good and i recommand to stay back. Every one in this world do not get jobs in good/big companies like my friend gets, you know the ratio of available candidates is very big. If you find one than think.
This offer of 16.5K is same as that of indian & you have to make your own accomodation which shall cost minimum Qr.5000/- pm, its your wish to choose . . .
Ya! you can enjoy some time here with a multi-national culture at work and around with family, these will be the benifits. But remember Qatar in particular apart from other GCC countries is full of politics at work place.
Try your luck !