We present a theoretical model for describing the electric field-driven migration and dispersion of short anisotropic molecules in nanofluidic filter arrays. The model uses macrotransport theory to derive exact integral-form expressions for the effective mobility and diffusivity of Brownian particles moving in an effective one-dimensional energy landscape. The latter is obtained by modeling the anisotropic molecules as point-sized Brownian particles with their orientational degrees of freedom accounted for by an entropy penalty term, and using a systematic projection procedure for reducing the system dimensionality to the device axial dimension. Our analytical results provide guidance for the design and optimization of nanofluidic separation systems without the need for complex numerical simulations. Comparison with numerical solution of the macrotransport equations in the actual, effectively two-dimensional, geometry shows that the one-dimensional model faithfully describes the field-and size-dependences of mobility and diffusivity, with maximum difference on the order of 10% under the experimentally relevant electric fields.