  We study strongly correlated ground and excited states of rotating quasi-2D
Fermi gases constituted of a small number of dipole-dipole interacting
particles with dipole moments polarized perpendicular to the plane of motion.
As the number of atoms grows, the system enters {\it an intermediate regime},
where ground states are subject to a competition between distinct bulk-edge
configurations. This effect obscures their description in terms of composite
fermions and leads to the appearance of novel composite fermion quasi-hole
states. In the presence of dipolar interactions, the principal Laughlin state
at filling $\nu=1/3$ exhibits a substantial energy gap for neutral (total
angular momentum conserving) excitations, and is well-described as an
incompressible Fermi liquid. Instead, at lower fillings, the ground state
structure favors crystalline order.
