Error accumulation is a fundamental limitation of any hereditary polymer. Canonical duplex DNA mitigates replication noise through enzymatic proofreading and repair, but remains vulnerable to independent, local errors. In this work, I develop a theoretical framework for mutation, noise, and error correction in Q-DNA, defined as a canonical tetra-stranded hereditary polymer. I show that tetra-strand coupling generically produces correlated error patterns and enables structural and topological error-correction mechanisms unavailable to duplex systems. I derive theoretical error rates under correlated noise, analyze majority- and consensus-based correction schemes, and identify structural motifs capable of intrinsic self-correction. These results position Q-DNA as a system in which error correction may be partially embedded in geometry and topology rather than relying exclusively on enzymatic machinery.