I assume you're using pfsense's inbuilt dnsmasq to perform DHCP and DNS duties? I don't think dnsmasq supports anything resembling HA or failover, so bear in mind that what follows will be vastly more complicated than that.
Yeah ISC dhcpd supports failover natively. I don't run it myself (and years since I did it at work) but there's a (perhaps slightly outdated) tutorial on this
here that's quite nice and easy to follow.
On a similar note, it's quite common to provide HA (but not failover) by having two DHCP servers, each serving half of the network segment. For instance, if you've got a network 10.11.12.0/23, dhcpdA might be configured to dish out addresses 10.11.12.1-255 and dhcpdB might be configured to dish out addresses 10.11.13.0-254 - that way even if one of your DHCP servers goes down you should still have half of your range accessible - but this sort of setup plays merry hell with things like static DHCP reservations, so it's really only useful for large ad-hoc networks where static configs won't be needed.
bind/dhcpd doesn't really have the same sort of thing because DNS is meant to be redundant by default - you should be able to configure two identical SOAs that should both be able to function independently of one another. Just set up two name servers that are authorative for examplezone.local or whatever and both should be able to function - but this can make things like DDNS via DHCP problematic as well since you'd now need to be updating two zones rather than one.
I'm cheating in this regard and using Samba with a bind DLZ; the DNS configuration is actually stored on all my domain controllers (which handle the multi-master replication) and that's presented through bind via the DLZ.
Going back to basics, it might be able to keep using pfsense dnsmasq as your primary and scripting something to pull info out of the dnsmasq config and copy to another dnsmasq instance elsewhere... and a quick bit o' google-fu turned up a project that already aim to try doing this...
GitHub - spops/dnsmasq-ha: dnsmasq failover (keepalived)
GitHub - jiasir/dnsmasq-ha: dnsmasq failover (keepalived)
...albeit looking like some seriously horrible wrangling with apt commands, essentially installing/uninstalling to achieve fake HA. Yeuch!