While quantum computing might not be a threat to bitcoin directly, yet it is a threat to the security of funds when you reuse addresses. This is because when you use an address, your public key is exposes and with quantum computing, it can be possible to compute your private keys from your exposed public key.
It is better you don't reuse addresses, You can mitigate this risk by moving your funds to a new unused address each time you use an address so that your coins are safe in the new unused address.
I'm a little bit confused on this because, my wallet generates a new bitcoin address anytime I use it. So why would it be necessary to move my coins every time I use it? Isn't that the point of the wallet generating a new address every time it is used?
I guess you use a HD wallet. When your wallet generates a new address for you, it's for receiving a new transaction and to increase privacy. It does not automatically move the funds to a new address unless you choose to do it manually.
The new address is empty and your UTXOs remains in the old address, the main point is not to reuse the old address, next time you're accepting a pay, make use of the new address.
When there are multiple UTXOs, target a time the fees are low and consolidate some of the UTXOs in a new address to reduce fees when you want to send more funds across at a time.