We study rotating quasi-two-dimensional Fermi gases, in which atoms are interacting via dipole-blockaded potentials: repulsive dipolar potentials flattened at a distance below R.For rapid rotation, the characteristics of the dipole-blockaded interaction give rise to an interesting competition between the correlated crystal structure and the Laughlin liquid in the factional quantum Hall regime.We find that the correlated bubble crystals have lower energies than the Laughlin liquids for higher R values.The Laughlin liquids are energetically favorable for rotating dipole-blockaded Fermi gases in the lowest Landau level only when the filling factor and the blockade radius R are higher and smaller, respectively.