POST-based searches are rather inconvenient, as there's no easy way of saving the search page. As far as I'm aware, referer headers are still sent to HTTPS links, even if the origin differs. So https://duckduckgo.com would still send referers to https://example.com.

But if you still don't want your clicks going through the r.duckduckgo.com domain, you can turn it off in the settings.

Presumably you also disable Javascript by default, right?