Two-dimensional (2D) metal-halide perovskites are attractive for use in light harvesting and light emitting devices, presenting improved stability as compared to the more conventional three-dimensional perovskite phases. Significant attention has been paid to influencing the layer orientation of 2D perovskite phases, with the charge-carrier transport through the plane of the material being orders of magnitude more efficient than the interlayer transport. Importantly though, the thinnest members of the 2D perovskite family exhibit strong exciton binding energies, suggesting that interlayer energy transport mediated by dipole-dipole coupling may be relevant. We present transient microscopy measurements of the interlayer energy transport in the (PEA)2PbI4 perovskite. We find efficient interlayer exciton transport (0.06 cm2 s-1), which translates into a diffusion length that exceeds 100 nm and a sub-ps timescale for energy transfer. While still slower than the in-plane exciton transport (0.2 cm2 s-1), our results show that excitonic energy transport is considerably less anisotropic than charge-carrier transport for 2D perovskites.