We investigate liquid crystalline phases with nematic order at 1/3-filling of the valence Landau level (LL). We generalize Laughlin's fractional quantum Hall (QH) effect wavefunction at ν = 1/3 to include anisotropic nodal distribution by modifying the Jastrow factors. Lengthy Monte Carlo simulations are then used to determine with unprecedented accuracy the (anisotropic) pair distribution function g(r) and static structure factor S(q) for various degrees of anisotropy. The determination of the correlation energies at 1/3-filling of an arbitrary LL is then performed by using standard mappings of g(r) and S(q) to higher LLs. Our results indicate that while Laughlin's state is stable in the lowest LL, there are regions of instability towards nematic order in higher LLs. Possible connections to the recently discovered QH liquid crystals are discussed.