How heavy is the DNS used for changes (records added/removed)? Do you have DNSSEC active? Does the DNS server also act as a caching DNS (given that you mention it as an external DNS, I suppose not)? These things can influence the specs of the server.

I would imagine that, for common use cases, low specs are fine, but as this is an external facing DNS server you probably cannot be certain that more interaction won't happen. If too lightweight, a lightweight DDoS might be sufficient to bring it down, which majorly impacts your service. So I wouldn't go below 2core, 4Gb.

But personally, I don't recommend hosting your own DNS. DNS is a brittle service the moment you want to do more than just exposing a single zone, and the complete DNS architecture shouldn't rest on a single service. There are dedicated DNS service providers out there that work very well, and can be programmatically configured (API).