I am giving you the figures which may give you an idea about cost of living in Qatar for couple(No Kids).

QAR (Per Month) For 2 Persons
4,500 House Rent (Furnished)1 BHK appartment
1,500 Groceries+ Misc exps.
1,600 Car Hire / OR Loan installment + Petrol
33 Land Line Rent
50 Mobile Rent OR Prepaid Card
100 Water Charges
100 Electricity
200 Internet at home
75 Television Channel Connection
120 VOIP Call Card to call home country
200 Car Insurance (2500/12)if you own your car
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8,478 Total
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One Time Exps.
1,000 Deposit for Water Connection
1,000 Deposit for Ele. Connection
4,500 House Rent Deposit
2,000 Driving Classes Fees (Appx.)
250 One Time Mobile activation Charges
_____________________
8,750 Total
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Not included Medical Insurance & Return Air Fare for family once in a year as most of the companies are taking care of it.

Medical Facilities are very costly here.

Wish you all the best.