We discuss an experimental feasibility of fractional quantum Hall-like and Wigner crystal-like states in ultracold two-dimensional rapidly rotating polarized dipolar Fermi gases. In particular, we argue that the ground state of the system at filling factor 1/3 is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. For low filling factors, we demonstrate the stability of a crystal state and indicate the possibility of a quantum phase transition from Laughlin liquid into Wigner crystal. |