  We systematically develop a density functional description for the
equilibrium properties of a two-dimensional, harmonically trapped,
spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizs\"acker
approximation. We pay particular attention to the construction of the
two-dimensional kinetic energy functional, where corrections beyond the local
density approximation must be motivated with care. We also present an intuitive
derivation of the interaction energy functional associated with the dipolar
interactions, and provide physical insight into why it can be represented as a
local functional. Finally, a simple, and highly efficient self-consistent
numerical procedure is developed to determine the equilibrium density of the
system for a range of dipole interaction strengths.
