In new MacOS, sending SIGINFO to mDNSResponder does not work:
$ log stream --predicate 'process == "mDNSResponder"' --info
...
Responder: [com.apple.mDNSResponder:Default] Sending SIGINFO to mDNSResponder daemon is deprecated. To trigger state dump, please use 'dns-sd -O', enter 'dns-sd -h' for more information

So as messages states, we can try dns-sd -O:
$ sudo dns-sd -O
XPC service returns error, description: State dump is only enabled in internal builds

I tried to check when this error occurs by looking into source code:
https://opensource.apple.com/source/mDNSResponder/mDNSResponder-1310.80.1/mDNSMacOSX/xpc_services/xpc_service_log_utility.c.auto.html

This error occurs when IsAppleInternalBuild() method is returning false. There is also comment:
	// We do not dump state in the customer build due to privacy consideration.

After looking at this method it looks like it can be changed.
This is how methods are being invoked:
handle_requests() -> IsAppleInternalBuild() -> os_variant_has_internal_diagnostics()

So we need to make sure that os_variant_has_internal_diagnostics() is returning true.
This method is in file:
https://opensource.apple.com/source/Libc/Libc-1244.1.7/libdarwin/variant.c.auto.html

After looking into this file it seems like to make it work, we need to:
1. Make file named /var/db/os_variant_override and make sure it is not empty (one space should be enough)
2. Make file named /System/Library/CoreServices/AppleInternalVariant.plist and copy content from here: https://opensource.apple.com/source/Libc/Libc-1244.1.7/libdarwin/AppleInternalVariant.plist.auto.html
3. Reboot system
4. Try running sudo dns-sd -O