Quad9 is a conglomorate of "Threat Intelligence Partners" and three founding organizations: IBM, Packet Clearing House and Global Cyber Alliance https://www.quad9.net/about/ . What's that third one? I don't know, but it's founded by The City of London Police, NY District Attorney and the Center for Internet Security https://www.globalcyberalliance.org/who-we-are/ that third one is like a hundred "Partners", with such privacy champions as The US Secret Service. Over 100 organizations. What are their incentives? What role do all these organization play and how much access do they have? Who knows.
Compare their privacy policies. They're strikingly similar because Quad9 largely lifted theirs from Google's (I'm assuming, since theirs came later)
https://developers.google.com/speed/public-dns/privacy
Google's policy states they collect private information for 24-48 hours, keep "anonymized" information for 2 weeks and then randomly samples that data for permanent storage:
> Google Public DNS stores two sets of logs: temporary and permanent. The temporary logs store the full IP address of the machine you're using. We have to do this so that we can spot potentially bad things like DDoS attacks and so we can fix problems, such as particular domains not showing up for specific users.
> We delete these temporary logs within 24 to 48 hours.
> In the permanent logs, we don't keep personally identifiable information or IP information. We do keep some location information (at the city/metro level) so that we can conduct debugging, analyze abuse phenomena. After keeping this data for two weeks, we randomly sample a small subset for permanent storage.
Quad9 collects effectively the same information (except AS) as Google's 2 week logs and says
> All the above data may be kept in full or partial form in permanent archives.
If you want a game theoretic, capitalist analysis, Google has an incentive to keep the web running and keeping it an awesome platform, to make sure humanity's information is created and shared in an open format that they know how to index and that they can freely index, instead of apps or some alternative web or some other walled garden.
But we're bombarded daily with "goog bad" by politicians and journalists, so Google must obviously be just brazenly lying and you should give your DNS history to an organization founded by The City of London Police instead that "share anonymized data on specific domains queried [...] with its threat intelligence partners".
Please double check my work, I didn't read the privacy policies too carefully (I think notably Google stores the AS number and Quad9 doesn't) because I don't actually care, I (along with roughly 100% of internet users) just give all my DNS history in plain text to my ISP.