Try Qatari Arab Company For Vegetable Production at Shahinaya. I have visited this place many years ago. They grow vegetables in huge green houses. At that time they were even growing strawberries.

Many Qataris have private farms, which are also very beautiful. We visited such a farm when our first child was just a few years old and have photos of him sitting surrounded by piles of tomatoes.

Some time back the local dairy producing companies were encouraging people to visit their farm, in order to generate loyalty for local brands over those imported from neighbouring countries. Try to get in touch with them.