I was working for my employer and holding a valid...

We would like to inform you that according to the Qatari Labor Law, if you have residence in Qatar and want to end it or the employer terminated you and that cause cancelling the residence, and you sponsored your family, then after cancelling the residence the family residence will be cancelled to. So they have to leave the country with you and they can't stay in the country if the wife didn't change the residence on her employer.
Note that the sponsorship is not applied anymore there and it is cancelled then the relation between the employer and the worker is according to the work contract.
Article 21:
The employer, the Competent Authorities, and the Ministry of Labor and Social Affairs may agree to transfer the Foreign National laborer to another employer before the time limit in the contract has been reached or after five years of working for the employer if the contract did not specify a time period.
The Foreign National laborer may, with authorization from the Competent Authorities and the Ministry of Labor and Social Affairs, transfer to another employer in the event of the Recruiter’s death or dissolution of the body corporate for any reason.
In all cases, the employer serving as the Recruiter shall not have his legal rights, or the contract between him and Foreign National, violated, in accordance with the referenced Labor Law.
The aforementioned article organized the cases of which the employee can transfer to another company as follow:
• With an approval from the employer (Whatever the contract is)
• After completing five years on unfixed term contract
• The end of the fixed term contract
• The death of the employer
Therefore, you can transfer if your employer agrees then you have to submit your resignation or it may result in depriving you from entering the country once again for a year.