dnscrypt-proxy also supports DNS-over-HTTPS and is probably the most popular DoH client.

You can use it to connect to Cloudflare or other DoH servers, and this will not be limited to queries sent by Firefox.

On iOS, use DNSCloak.

"On the Firefox network and security teams, we’re working to change that by encrypting DNS queries and by testing a service that keeps DNS providers from collecting and sharing your browsing history."

Adding an authentication header prevents alteration but it does not present a viable option to the problem statement.