You can use ODoH (https://blog.cloudflare.com/oblivious-dns/) to double-encrypt your DNS requests and forward them through an external server, disconnecting your query from your response, and encrypting your upstream DNS requests. You can pick any relay from this list: https://download.dnscrypt.info/dnscrypt-resolvers/v3/odoh-re... (need to de-base64 them to get the actual domain) and any upstream DOH server you prefer.
This isn't effective against DNS-level censorship, though. A DNSSEC validation error is just as effective as a fake NXDOMAIN or bogus IP at keeping me from visiting the correct site.
You will have issues because your DNS is slow or dead :)
By leveraging Oblivious DOH you can even encrypt your DNS traffic securely to your upstream DNS provider without having to set up your own recursive resolver (which would only lead to privacy issues).
Every hop adds latency, though, so I'd recommend using as direct a connection as you can get. DNS latency can make your internet experience a real pain!
Who knows if some 'suspicious' DNS queries sent to Google will accidentally set off some tripwire that causes them to lock you out of half the internet: https://news.ycombinator.com/item?id=30771057
I'm still trying to add http3 to my DNS server and can't test DoH. But based on the other comments, it looks like a custom DNS server will use DoH if supported?