Millimeter-wave using large-antenna arrays is a key technological component for the future cellular systems, where it is expected that hybrid beamforming along with quantized phase shifters will be used due to their implementation and cost efficiency. In this paper, we investigate the efficacy of full-duplex mmWave communication with hybrid beamforming using low-resolution phase shifters. We assume that the self-interference can be sufficiently cancelled by a combination of propagation domain and digital self-interference techniques, without any analog self-interference cancellation. We formulate the problem of joint self-interference suppression and downlink beamforming as a mixed-integer nonconvex joint optimization problem. We propose LowRes, a near-to-optimal solution using penalty dual decomposition. Numerical results indicate that LowRes using low-resolution phase shifters perform within 3% of the optimal solution that uses infinite phase shifter resolution. Moreover, even a single quantization bit outperforms half-duplex transmissions, respectively by 29% and 10% for both low and high residual self-interference scenarios, and for a wide range of practical antenna to radio-chain ratios. Thus, we conclude that 1-bit phase shifters suffice for full-duplex millimeter-wave communications, without requiring any additional new analog hardware.