We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the statistics of the laser threshold and linewidth (lifetime and Petermann factor of the resonances) when the resonator is filled with an active medium. The laser threshold decreases for increasing refractive index n and is smaller for TM polarization than for TE polarization, but is almost independent of the number of out-coupling modes N. The Petermann factor in the linewidth of the longest-living resonance also decreases for increasing n and scales as sqrt(N), but is less sensitive to polarization. For resonances of intermediate lifetime, the Petermann factor scales linearly with N. These qualitative parametric dependencies are consistent with the random-matrix theory of resonators with small openings. However, for a small refractive index where the resonators are very open, the details of the statistics become nonuniversal. This is demonstrated by comparison with a particular dynamical model.