A previously developed Gabor-based quasi-ray narrow-waisted (NW) Gaussian beam (GB) algorithm for time-harmonic propagation of aperture-excited two-dimensional (2-D) electromagnetic fields through a planar dielectric layer is extended here to the time domain (TD) to deal with short-pulse excitation. The dielectric layer is assumed to be nondispersive; however, slight Ohmic losses can be accommodated. The frequency domain (FD) algorithm is based on a self-consistent discretization of the aperture field distribution in terms of basis NW-GBs in conjunction with an efficient quasireal ray tracing scheme for tracking the individual basis beams. The TD results are obtained by analytic Fourier inversion from the FD in terms of pulsed beam wavepackets, following a procedure similar to that utilized by Galdi et al. (see IEEE Trans. Antennas Propagat., vol.49, p.1322-32, Sept. 2001) in connection with free-space aperture radiation. The proposed algorithm is validated and calibrated against a rigorous numerical reference solution via an extensive series of numerical experiments. A priori accuracy assessments in terms of critical nondimensional estimators, and computational costs, are also given attention.