Three months is the grace period after the expiry of work visa. After that there is penalty of QR 10 per day for each day after the visa expiry. If your company is not planning to extend your work visa, why go through the trouble of applying for their residence visa? However, as MM has very rightly said, projects do get delayed and you could begin the process of family residence visa. I believe your family's visit visa could be extended up to six months.