In that case, the HTTP part would probably just be working against you. Fortunately, people are working on DNS over QUIC:
https://datatracker.ietf.org/doc/draft-huitema-quic-dnsoquic...
https://datatracker.ietf.org/doc/draft-huitema-quic-dnsoquic...
For many use-cases, that penalty will be paid on every request rather than just the first request, because many DNS resolution libraries aren't designed to have persistent state, so every time the library is used, it will have to set up a new connection to the server from scratch.
Also, tls1.3 adds 0rtt for subsequent cqlls to the same server.