Traveling with Newborn

I'm a Canadian citizen and my husband is an American citizen. I am visiting him in Texas for 6 months and I'm having a baby down here. The baby will be an American citizen, but a few months after the baby is born I have to go back to Canada.
I have a pending I-130 in progress to get my American greencard, but until it gets approved, I have to remain in Canada unless I'm visiting.
My question is; Since I have to go back to Canada after the baby is born, will they allow me to take the baby with me? What documents will I need to present at the boarder? And how long will it take to get those documents processed?

If you've filed the I-130 already, I doubt it's going to take six more months to get to interview stage, although the Texas Service Center is notoriously slow. So you may get caught on the hop by the interview date.

You certainly can legally visit while the I-130 is pending, although CBP I suspect are going to be suspicious of a pregnant woman visiting her US husband, especially for a long period. Take minimal luggage and cast-iron proof you intend to return to Canada, I would suggest.

You can also can take the baby back to Canada with you, but you need the consent of the father and it's a good idea to have it in writing with his contact details.

Entry procedure into Canada is the same as for anyone else, at the moment babies accompanied by their parents only need a birth certificate at a land border. Otherwise a passport, a baby can't get a NEXUS card. You can apply for a citizenship certificate for the baby but given that you'll only be coming back briefly you may not want to do it: http://www.cic.gc.ca/english/citizenship/proof-how.asp

The baby can re-enter the US with the birth certificate also.

I'm already in Texas. I had no problems getting into the country just to visit. I didn't look pregnant and I had my return trip ticket handy.
How long does it normally take to get a birth certificate for a baby?

ask the hospital where you plan to give birth.