Unfortunately, it is really mandatory for anyone working in Bahrain or anywhere in the GCC to first have his or her residence/working visa cancelled before being given a residence permit here in Qatar.

Go have a proper talk with your employer and request them (in a nice way, of course) to let you go so you can provide better for your family. Tell them that you wish the company well and promise them that you would continue to help them out if there's anything that you can do for them while you are in Doha.

Good luck!