I wrote something similar using Google's dns-over-https
https://github.com/aaron10/https_dns_proxy
Can install in seconds on openwrt/lede with "opkg install https_dns_proxy" and a few tweaks to /etc/config/dhcp. Does a lookup over regular DNS to get the IP of dns.google.com then routes all requests through a set of http/2 pipelined connections to Google. Still need something like dnsmasq as it isn't a caching proxy.
