We don't think that QC development will happen step by step. Our expectation is that someone will find a QC technology, that allows "far beyond expectations" numbers of qubits, that will allow this QC to get all private keys immediately.
We think that such a QC will surprise the Bitcoin community and only thereafter we will upgrade to a quantum resistant Bitcoin network. We hope that the user of such a QC to get the private keys, knows exactly how Bitcoin works and allows the owners to transfer their coins to the new QC resistant addresses. It would be a win-win game: the QC user would get the "lost" coins, the Bitcoin owners could transfer their coins to QC resistant addresses, the Bitcoin ecosystem wouldn't be affected, we would have a stronger Bitcoin network. How would a QC user act: starting with the oldest "lost" coins and moving them, so that the Bitcoin community can realize that someone is moving the "lost" coins (e.g. a special posting board here on bitcointalk) but gives the owners the possibility to transfer their coins to other addresses. In the meantime we will have a very quick "quantum resistance upgrade". And it will continue like DannyHamilton described it:
but stronger