Most airlines will politely refuse if you try to check-in with a child that is less that two weeks old (the ones which do not politely refuse are somewhat ruder). Even though airlines have a lot of freedom in setting the rules for whom they allow to travel, the rule of newborn children seems to be universal.
Not that it is bad, mind you. On the contrary, that is a great idea. A newborn child has not yet got used to being outside the safe, warm, quiet and dark environment of the womb. Why put them in an aluminum tube with bright lights and lots of noise?
The noise may not be such a bad idea, actually. Newborn children crave the constant background white noise of their mothers heartbeat, and the noise of an airplane engine is the right kind of "white noise" that can lull children to sleep. Most parents have stories about washing machines, vacuum cleaners or dishwashers putting their children to sleep by calming them. The white noise from the engines in the airplane is the same kind of white noise that a washing machine gives off.
If the airplane was a dark, moist place where you could have bodily contact with your parents, then it would be a different matter. But the reason you should not let a newborn child travel is not that the airplane is a noisy environment. It is the rest of the airplane environment that is harmful.
Just consider: Here you have someone whose immune system has not encountered anything harmful before. Nothing, in fact. Not even a single bacterium and certainly not a lot of virii. The baby does not know anything about the world, and it does not know what is harmful. Its immune system is just being prepped on how to handle the dangers of the real world, and then you put them in an environment where they have to breathe the air recycled from other passengers for at least an hour (usually more like four, but frequently six or seven). Which includes bacteria and viruses.
And that is not the only problem with the airplane air. It is colder than the child is used to (which was body temperature), so you have to swaddle it in blankets. Newborn are small enough to ride in the bassinets which attach to the airplane wall, if you wrap them up properly.
The other problem about the air of the airplane is not that it is cold, it is that it is dry. Newborn children do not yet have the proper mechanisms in place to moisturize the membranes of their nose and mouth (not even their lungs), and the main way for getting fluids is by drinking breast milk (or baby formula). They quickly get full and do not want to give them more. You can give them water, but it passes right through. But if they do not drink, they get dehydrated.
On the whole, very small children are too vulnerable to all the dangers of a flight (and I have not even mentioned check-in and boarding). Most countries will also not give passports to children before they are a couple of months old, which means most countries will not allow them to travel by definition - since airlines are required to have identification from all passengers.
And then, I have not even mentioned the stress to the mother. Giving birth to a child is a major labor (pun intended), and any woman needs a few days to recover, if not more.
Considering all these things, it is better to stay at home with your children while they are small. Park your wanderlust for a few months. And plan for the first trip with your baby - their tickets will be free until age 2.
I am Wisterian Watertree, recently moved from Tokyo to Sendai, previously of Bangkong and Honolulu. I write about travel, especially with our three beautiful kids (two girls and one boy, soon turning seven - yes. they are triplets). Travel is education and fun rolled into one, and if you are like me, that is something you want to give to your kids. If you want more tips and want to find out when I will publish something, get it from my email list. If you want to be personal, drop me a note on firstname.lastname@example.org, or if you want general tips, follow me on Twitter @wisterianw.