I hope baby have seprate passport,well matter is easy.just attest birth certificate from local authority and qatar embassy in Washington,there is mission in Nyc also, this is what we do in our country, Since us citizen dsnt need visa so you can bring directly but I think you have to get return ticket that you can use later or can get refund.one thing is sure there will be no problem at all to enter and getting rp at your sponsorship
I hope it is lovly to see your baby in your hand for you.
good luck