Use dnsmasq for DNS

As the name already implies, dnsmasq is not a full-fledged DNS server. If you want a real, recursive DNS resolver, consider using unbound instead.

Install dnsmasq

dnsmasq is available on SailfishOS chum. You 1st need to add the 3rd-party-repo, afterwards running devel-su pkcon refresh && pkcon install dnsmasq will install it.

Disable your current DNS handler

On a fresh installation, DNS is handled by connman. You can remove it with these instructions.

Permanently run dnsmasq on boot

Execute devel-su systemctl enable --now dnsmasq to enable it permanently & start it now.

Configure dnsmasq

dnsmasq's configuration lies under /etc/dnsmasq.conf. You can get more information about its config options from dnsmasq's manpage and ArchWiki.