Once you get his passport, just process his visa/Resident permit. there is no ID card issued for children only need to put RP/visa sticker on passport. so that he can re-enter Qatar.

For visa/RP processing, HR/PRO of your company can do it for you provided you give them documents like photo,passport,birthcertificate,copies of your and wife,s ID/RP, filled and signed visa form etc.