While all the info I have been able to read does point to vaping not being dangerous to the user (who is an adult) I have yet to see any research on what you can actually consume from secondhand vapor. Granted the vapor is a million times better than smoke but to say that the users around you will not get any of your vapor is ignorant (and if you go to a big vape meet and get hit with all of the nicotine in the air you will know how much you can get secondhand). Just because something is safe for an adult doesn't mean it is safe for a child or especially an infant.
I would personally not vape around a young child, the fact that it could expose them to nicotine being only one of the reasons. Teenagers it is probably not a big deal from a health stand point but it could get them to want to try it (which is good if they were going to smoke tobacco anyway but if they didn't want to try tobacco but want to try vaping idk if that is a good thing or not).
Just one of those rather error on the side of caution.