Visa application for newborn

My wife and I currently live in the US (we are not US citizens), and we may move to Canada on September for me to take a job as postdoctoral fellow for one or two years. My problem is that my wife is pregnant and the baby is due only 4 to 6 weeks before we will have to move. My concern is whether we will have enough time to get our newborn baby her US passport (which supposedly should take a couple of weeks, though we probably can't get it until after a couple of weeks after she is born), and then getting her Canadian visa. I don't really know how this would work, I'm assuming that my wife and I would apply for the visa several months in advance and then we would need to add our baby. I'm also not sure whether it helps that our baby will be a US citizen, may it be that she'll be able to enter Canada with us even if she doesn't have a visa, and then go through the paperwork once we already are there? Any help is appreciated...