The first entities that are likely to achieve practical quantum computers will either be governments or big tech companies like Google. And it will be a big deal, so there would likely be several years of warning before it could be at the point where it would make sense to use it to steal someone's bitcoins (I guess the original Satoshi coin address would be the biggest bounty). And in the time period between when the big development is first announced and before it's practical, Bitcoin and other cryptocurrency projects can do a fork to a new digital signature scheme that is quantum proof (such as LegRoast) so that anyone who is concerned can move their coins to a new secure address. So while it would certainly be disruptive, it wouldn't necessarily spell the doom of Bitcoin.
Depends on the incentives. If the only interest in quantum computing is to break classically hard encryption then I think the time between poc and widespread availability could be relatively short.