This would be difficult to start as it would require trust. I already do exactly this ("white hat doxing") but do you trust that that is actually what I'm doing? Maybe it would be easier as an established corporation with an explicit privacy policy.
>I've been wondering if it is possible to dox my Reddit account.
You can make it much more time consuming and more difficult (read: but not impossible) to do so by using this userscript as frequently as possible: https://greasyfork.org/en/scripts/10380-reddit-overwrite
I personally run it for all posts older than 2~3 weeks (when activity/relevance of the post is nearly equivalent to "0").
Some sites still archive posts w/o updating for any future edits, there is web cache, etc. But those are far harder to search and tie together than simply browsing your comments on your profile. Note that some subreddits may ban you for using it and you'll get a bunch of AutoModerator posts asking you not to do that because of thread integrity and blah blah blah.