So what makes blockchain resistant to Quantum computing? Is it just having the ledger saved everywhere?
Quantum computing isn't like a magic wand that you can simply wave at cryptography to break it. It is just that there are certain mathematical problems that can be solved significantly faster using quantum processing as opposed to current processors. Some of these mathematical problems apply to Bitcoin and are thus potentially vulnerable to quantum computing. Luckily however Bitcoin also contains mathematical problems for which quantum processors don't have an edge over current processors.
This is quite possible and scary. Right now it is impossible to decrypt private keys, however it could be possible going forward that private keys could easily be decrypted by quantum computers - even instantly. Thus is the nature of quantum mechanics... nothing really makes much sense.
Nothing is instant and even quantum computers require the public key before being able to derive the private key eventually. Luckily the public key of an address is not known until the first transaction has been made, ie. your coins should be quantum safe as long as you refrain from reusing addresses.
It is very easy for Bitcoin developers to replace actual SHA-256 algorithm with a much more resistant SHA-1024 for example. There is no need to worry about quantum computers.
Even if Sha256 remains the PoW hashing algorithm of choice for Bitcoin, quantum computers would likely simply displace ASICs as mining hardware of choice. Why attack a blockchain if you might as well just mine it?