Gulf Times

OR the UNHCR (United Nations High Commission for Refugees)

No one can or will help you. Even if you go to the court there are many loopholes that the landlord can exploit them for his interests.

Honestly speaking you cannot protest as per the Qatar Laws.
Unions are against Qatar Laws.
Going to the police is not an option as they are the ones who kicked you out.

Here is my suggestion
Go to a mosque where rich Qatari sheikhs come and ask the Imam to tell them of your plight in his sermon and pray to God Almighty