Your query has really confused me. If your baby was born in Qatar...the RP process should have been done within the first month. If baby was born at your home country, why still there? Did your wife leave the child with relatives and joined you back? as your wife couldn't stay for more than six months outside Qatar...right?
Anyways...Go to the immigration office...fill up the form with the help of the typists there...bring along all the papers like birth certificate, passport of child (if seperate passport holder), your & your wife's passport copies, RP copies, marriage certificate (Optional) & two photographs of the child. Submit the documents at the counter and you would get the visa probably the same day....if not then the next day. Hope it helps... :-)