Ethereum is potentially quantum-resistant, as is any Turing-Complete cryptocurrency platform/network/whatever-you-call-it. Since you can implement your own cryptography, you can use use quantum-resistant ones.

It would still be a crypto-world catastrophe if modern non-quantum resistant crypto was broken. Essentially, everyone would have to deliberately move their coins in one fashion or another from a vulnerable address/account to a safe one--and can you imagine trying to herd that many cats?