Interesting thing to start, but before you go further, I would like to mention two important points:
1- Quantum computing era is not just about quantum hardware, it may become viable to see a lot of new quantum algorithms that may work much more effective in breaking cryptos than what hypothetically exist now, so a bit more reliance on academic work before designing anything is advisable.
2- Up to point 1 and the fact that it will take a lot more serious work than a routine coding project, it is much wiser to look after more effective way of designing the hashing-node network topology (51% attack) and also more stable economic model (better supply-demand difficulty adjustment and POS)
I'm not saying I know how to build this coin, nor that I'm going to do it now ... just starting a thread.
I agree that we will need to gather up the best of breed academic work about how to build quantum-resistant algorithms.
I wouldn't put any proof of stake algorithms in this ... KISS. Let's make a simple coin with just one major parameter changed - the hashing algorithm (we can also do faster confirms like Litecoin ... why not). Adding POS just complicates things. The next coins after QRCoin can add other features like POS.