Is there any law in Qatar that protects any employees for unlawful termination or termination without due process?

Sure there will be. I have no idea about your country laws, but definitely there will be provisions for protection of employees against unlawful termination especially when is not followed due process. Otherwise, you can surely sue the company for such cause of action in civil suit for seeking to put you back or reinstate you for specific performance or for the compensation. I would look forward the answers from our local friends over there to point out the exact statute an provision for your problem. Thanks.