Go through the Qatar Labor Law if you haven't already. This can be found on the following link...

http://portal.www.gov.qa/wps/wcm/connect/5f30f680423f8a149631df3cb857e4c...

I hope you'll find your answers. Article 49 appears to be relevant to you.
Even if your husband gets an NOC, he needs to take an exit before he could join a different employer. Which, unfortunately, means that you will have to accompany him along with your child since you and your child are under his sponsorship. I think without going into the legalities of what his current employer can or can't do, he should start looking for a job, ideally with a family status. If he has worked in Qatar for any length of time he'll get preference over those who are coming to Qatar for the first time. Once he finds a job with visa, he can leave and come back to his new employer. Of course your child's schooling may be jeopardized but if you are lucky enough and your husbands gets a family status as well, both of you can come back along with your husband and master junior can go back to the same school. The key is being +ve. Good Luck.