We fabricate a few-layer molybdenum disulfide (MoS₂) polymer composite saturable absorber by liquid-phase exfoliation, and use this to passively Q-switch an ytterbium-doped fiber laser, tunable from 1030 to 1070 nm. Self-starting Q-switching generates 2.88 μs pulses at 74 kHz repetition rate, with over 100 nJ pulse energy. We propose a mechanism, based on edge states within the bandgap, responsible for the wideband nonlinear optical absorption exhibited by our few-layer MoS₂ sample, despite operating at photon energies lower than the material bandgap.