i think you're having a wrong picture in your mind. if your baby is born in qatar, he/she will NOT be issued with VISIT VISA. visit visa is issued only to a person outside qatar and for the purpose of visiting.

if you have done the birth certificate and have signed the documents at CID (due to 2 sponsers for you and your wife), your baby is issued with the RP.

I think it's better you show your babys RP (or visa as you say) to somebody who can read arabic and get confirmed.