I have dual UAE and Qatar residences. Just go through the procedure as you normally do to get your Qatar residency. The last stage where you have to pay for the fee and glue the stamp on your passport, they will ask if you want to keep dual residency. If you do, then there will be an additional 2,000 QAR. I believe this expense is not the company's responsibility.

For your spouse/children, you will do the same.

Good Luck