DNSSEC, being based on UDP with a maximum packet length of 1232 bytes, is just one of many use cases where the deployment of post-quantum cryptography is going to require major protocol adaptations and in this case the introduction of request-based fragmentation to send the larger post-quantum public keys and signatures over UDP.
https://www.douglas.stebila.ca/research/papers/EPRINT-GoeSte22/
Note that in this case we care about signing, not encryption. (Well, signing and hashing (for subdomain name masking), but ttbomk most hashes we use are quantum-secure).
If you did that, you would end up with something that requires less computation to break using currently-known primitives.