If I am an employer,I will send you home immediately without giving you an NOC and/or ban you to work in Qatar ever because, you only use my company to find another work elsewhere.

Honestly, the moment you have your ID, you can't transfer to another company because of the regulation. However, if your employer is kind enough, he can give you a release and/or NOC to work in another company.

Whether you are a hot candidate, your transfer to another company depends on the kindness of your sponsor.

I suggest, stay around and when you finished your contract you can talk to your employer.

Have a sense of professionalism and work ethics because jumping from one company to another will not make you any good.