Yes, Toyota is no doubt the market leader. And I guess you will be able to find several models and types to suit your requirements. Just write to the Toyota agents in Doha to email to you their catalog on the type of vehicles you desire and you can select. The agent for Toyota in Qatar is Abdullah Abdulghani & Bros. Once you have made the selection, you can talk to them on leasing the vehicles. I believe the agents don't lease vehicles. You may then talk to rent-a-car companies.
Other than Toyota, Nissan and Honda also have a good share of the market. You can check with their agents also.