DNS is a very light protocol. In addition, responses tend to be cached, so it's not like the Pi would be hit with a dozen queries on literally every page load for every client on the network.
As @theandrewbailey mentioned, DNS is light protocol, I guess even older PIs would handle it pretty well. But, as a permanent solution, I would opt to set up on a VM/Docker so that I could have snapshots to quickly recover the service in the event of a problem.