For reference, there are some promising candidate for quantum resistant cryptography signature, such as :
1. Lamport Signature
2. Lattice-based Cryptography
3. Multivariate-based cryptography
These would be temporary solutions. Therefore they are developing new cryptos.
Postquantum, nobody will be able to prove that he/she/they was/were the owner/s in the old system, because everyone will be able to reproduce the privatekeys
of old blockchains.
We will have a quantum secure network.
This will be the new beginning.
It's partially wrong, ECDSA is partially secure against quantum computer as long as the public key of an bitcoin address isn't known.
The real risks is when quantum computer is fast enough to obtain private key from public key in few minutes, which allow double-spend or re-org attack.
Using new cryptocurrency which only use quantum resistant cryptography isn't bad idea, but :
1. Is moving to different cryptocurrency every-time when there's known critical/unfixable vulnerability on current cryptocurrency is good solution?
2. Some cryptocurrency is dominated by developer and investor (with pre-mine and coin distribution) which makes wealth distribution far worse than Bitcoin or today's fiat.