We don't know whether quantum computers will exist or not, but assume they will be built and some QC owners will move the early mined coins. What will happen?
The fact is everything evolves, if there is a technology that will attack certain protocols then it will evolve, if someone creates a Quantum Computer then they will plan to something that will benefit them rather than destroying something, that been said you need not worry about one in the next 20 years.
But you shouldn't fear from quantum computer. It is still hard to hack any crypto wallets. And also quantum computers can mine cryptocurrencies faster than ever.
The time interval does not change

and the price is not affordable to built a Quantum Computer to mine
BTCitcoin and even if someone creates i doubt it will be able to overpower all the hashing power around the world and hence it is an impossible task. If someone is creating specifically to mine
BTCitcoin then he must be really crazy and have a few millions at his disposal.