....like a Privacy-Respectful DNS.

The only thing which may work is a caching dns on localhost, like pdnsd, unbound and more. Using a cache DNS on localhost you are NOT doing queries, making impossible to track them. Sure, you do query your own DNS, from time to time your PC still does some recursive query , but this is not enough to profile you. They can't see how often you are using the record, neither build a time-series.

1.1.1.1, much like 8.8.8.8, lulls people into a false sense of security .

Caching proxies are the only answer to traffic analysis and timeseries profiling.