Switch firefox to use a different DNS than what is in the windows.host file

DNS resolving is usually done at the system level and not at the application level, so you can't normally have one program use one dns and another program use a different dns. I'm not aware of any firefox extensions that allow you to use a different dns.

It appears from your question that you already have a second set of DNS servers available that reference the development site instead of the live site.

I would suggest that you simply run a standard SOCKS proxy either on that DNS server system or on a low-end spare system and have that system configured to use the development DNS server. You can then tell Firefox to use that proxy instead of downloading pages directly.

Doing it this way, the actual DNS lookups will be done on the proxy machine and not on the machine that's running the web browser.

It's now possible, with the DNS over HTTPS function:

Open Options, General, scroll to very bottom and open Network Settings,

On the very bottom, you can find DNS over HTTPS:

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You had to use about:config before to change this setting, here's for documentation:

Type about:config in firefox address bar.

search for: network.trr.uri

You can use one of the DNS servers below:

Cloudflare: https://cloudflare-dns.com/dns-query
Google: https://dns.google/dns-query
Secure DNS EU: https://doh.securedns.eu/dns-query
Quad 9: https://dns.quad9.net/dns-query

And set network.trr.mode to 1

Hijacked from here: https://www.ghacks.net/2018/04/02/configure-dns-over-https-in-firefox/

I use this to override system's DNS with localserver
in about:config
change this value:

network.dns.forceResolve

network.dns.ipv4OnlyDomains

network.dns.localDomains

with IP address of local DNS server (for exsample 192.168.1.88)
Sorry for my english