  A two-dimensional dipolar Fermi gas in harmonic trap under rotation is
studied by solving "ab initio" Kohn-Sham equations. The physical parameters
used match those of ultracold gas of fermionic $^{23}Na^{40}K$ molecules, a
prototype system of strongly interacting dipolar quantum matter, which has been
created very recently. We find that, as the critical rotational frequency is
approached and the system collapses into the lowest Landau level, an array of
tightly packed quantum vortices develops, in spite of the non-superfluid
character of the system. In this state the system looses axial symmetry, and
the fermionic cloud boundaries assume an almost perfect square shape. At higher
values of the filling factor the vortex lattice disappears, while the system
still exhibits square-shaped boundaries. At lower values of the filling factor
the fermions become instead localized in a "Wigner cluster" structure.
