Where can I find out more about IT companies/landscape in the Middle East, and Qatar in particular? Are they mainly third party solutions providers?

Hi.  Many are third party.   There are local Bahrani compaines, and others in the GCC; however, the trend is to use Western Companies, especially those with clearance in the government sectors, and using talent from the US.   Bahrain is stepping up with Fintech, and I've had a couple of compaines there contact me via Linkedin wanting to do JV's for regional work.   

Is there anything in particular you are looking for in your research?

You can check Bayt to see the companies in Qatar and this link to go through the IT companies that hiring now.

You can also check this site.

Not really third party solution providers but now a days the trend is setting to the third party solutions to avoid the employee accountability.