As I've mentioned to another commenter, Bitcoin relies only on the existence of an arbitrary DSA. Quantum computing-resistant DSAs have been known since the 1970s. I reckon that swapping out Bitcoin's current DSA with a quantum-resistant one would not count as a major overhaul. https://news.ycombinator.com/item?id=43113682
It would probably require a “hard fork,” which is generally considered to be a major change in the Bitcoin world.
All the best,