The only way you're going to get this kind of support w/ OEM/stock firmware (assuming it isn't there now) is to have some other local device that does support it serve as a proxy (e.g., pihole), then reconfigure DNS on the ASUS w/ the LAN ip of that device rather than public DNS servers.
Short of that, DoT/DoH support has to be built into the firmware since it involves encryption, which is NOT a part of standard DNS. And why Merlin is such a popular alternative.