This runs doh-client (https://github.com/LinkTed/doh-client) as a dns over https client at port 53. By default the resulting container will use Cloudflare as resolver but you should be able to use any DoH supporting server. For a good list take a look here.
docker run --name doh-client --rm -p 53:53 -p 53:53/udp flexo3001/doh-client
The default options are (which you can override with -e option):
LISTEN_ADDR "0.0.0.0:53"
REMOTE_ADDR "1.1.1.1:443"
DOMAIN "cloudflare-dns.com"
LOCATION_PATH "dns-query"