So RSA has some 10-20 years to go. Is there a quantum computing-proof encryption algorithm, or is it just a matter of increasing key lengths?
This is still an area of active research. For instance, there are learning-with-errors-based cryptosystems: https://en.wikipedia.org/wiki/Learning_with_errors#Use_in_cr... But such systems are based on the assumption that "this type of problem is probably hard even with quantum computers". I believe we don't have anything more "quantum-proof" than that..
And of course, there are cryptosystems with unconditional security. Such as OTP.