Full-duplex base-stations with half-duplex nodes, allowing simultaneous uplink and downlink from different nodes, have the potential to double the spectrum efficiency without adding additional complexity at mobile nodes. Hybrid beam forming is commonly used in millimeter wave systems for its implementation efficiency. An important element of hybrid beam-forming is quantized phase shifters. In this paper, we ask if low-resolution phase shifters suffice for beamforming-based full-duplex millimeter wave systems. We formulate the problem of joint design for both self-interference suppression and downlink beamforming as an optimization problem, which we solve using penalty dual decomposition to obtain a near-optimal solution. Numerical results indicate that low-resolution phase shifters can perform close to systems that use infinite phase shifter resolution, and that even a single quantization bit outperforms half-duplex transmissions in both low and high residual self-interference scenarios.