  A recent experimental realization of quantum degenerate gas of
$^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar
Fermi gases and many-body phenomena arising in that regime. Here we derive a
mean-field variational approach based on the Wigner function for the
description of ground-state properties of such systems. We show that the
stability of dipolar fermions in a general harmonic trap is universal as it
only depends on the trap aspect ratios and the dipoles' orientation. We
calculate the species-independent stability diagram and the deformation of the
Fermi surface (FS) for polarized molecules, whose electric dipoles are oriented
along a preferential direction. Compared to atomic magnetic species, the
stability of a molecular electric system turns out to strongly depend on its
geometry and the FS deformation significantly increases.
