yes, you can get extension for your family visa, for that you have to go to immigration department fill a form attached passport copies of your,your's wife & the child for whom you wanted to extend the visa.It will charge per person 500/-QR and your family residence permit should be valid .You can extend up to 6 months but it also depend upon the expiry date of your family visa i.e. if your family visa will expire after 4 months they will extend the period for 4 months only but the charges will be remain same.