Am thinking, you could install Zen load balancer (Debian based) on both nodes alongside Pi-Hole (way easier).
It will create a virtual interface for you (on the active node) on which you can publish the Pi-Hole services (DNS, HTTP, DHCP).
Advantage, you have a load balancer in your network (can load balance anything TCP/UDP) + you get warnings via push notifications if a node is non responsive and it will do failover for you.
Check out the free version:
https://www.zevenet.com/products/community/#repository
Ps. They renamed brand from Zen to Zevenet.
Ps2. If you go about load balancing something more network intensive, a RasPi will not be suitable anymore.