There is no precise definition of “doxxing” and that term is not used in the law at all. In general, doxxing seems to refer to gathering information about someone using available sources on the internet, at least as a starting point. There is nothing illegal about gathering up information that is freely available to everyone on the internet. If the person obtains information illegally, by say hacking into an account to which he is not allowed access, that may be a crime. So it depends very much on what the person does to gather the information. It also matters where the person is located as well as where whatever computers he/she is trying to access are located. So long as the person is not obtaining the information illegally, there isn't anything you can do to prevent him/her from gathering that info.
However, threats and harassment are another matter. Those things are not part of doxxing, though the information obtained might be used to engage in threats and harassment. Threats and harassment can be crimes, so if you are getting threats of violence or are subject to harassment, you will want to report that to police.
By and large it is a good idea to avoid direct confrontation with unknown people on the internet. You never know which person out there might be mentally unbalanced, violent, etc., and might take revenge against you for that confrontation. Outing that guy may not have been wise. If you really thought he might be involved with receiving or distributing child porn, report that to the FBI or local police and let them deal with it.

