You cant lease a car here, you either buy or rent. When you rent you cannot take it out of the country as the car is not in your name. If you have bought a car and it is on loan from the bank you also need a letter from the bank to be able to travel out of Qatar with it.

If you are planning a trip to Oman it may be in your best interest to fly and rent a car when you get there.

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"Diplomacy is the art of saying 'Nice doggie' until you can find a rock - Will Rogers"