How about traveling with a 4 month old puppy? Do they allow it?

Maybe but you really shouldn't do that to people or the animal.

If your airline allows it and you follow their rules then the airport does too. You should also go to the TSA website and look at their rules for traveling with pets.

You can, but I highly highly don't recommend don't that at all. They are still too young and it's very stressful for them, not to mention the possibility of them getting something because their immune system is not too great yet.