Proxmox Turnkey DNS Server

Looking here I can't see one. But you can also search in your Proxmox GUI by pressing the Templates button within a PVE Templates storage - which also shows that none exist.
 
I thought of loading dnsmasq
Perfectly feasible. I would do it in an LXC not on the Proxmox host.
As far as your main question - setting up a simple DNS server - you could do any of the simple AdGuard, pi-hole etc. in an LXC.
Search these forums & the general WWW for more info.

As a rule - don't go making any unnecessary changes to host services & configs on the PVE host node itself.