The detection of large quantities of dust in z ∼ 6 quasars by infrared and radio surveys presents puzzles for the formation and evolution of dust in these early systems. Previously, Li et al. showed that luminous quasars at z ≲ 6 can form through hierarchical mergers of gas-rich galaxies, and that these systems are expected to evolve from starburst through quasar phases. Here, we calculate the dust properties of simulated quasars and their progenitors using a three-dimensional Monte Carlo radiative transfer code, ART2 (All-wavelength Radiative Transfer with Adaptive Refinement Tree). ART 2 incorporates a radiative equilibrium algorithm which treats dust emission self-consistently, an adaptive grid method which can efficiently cover a large dynamic range in both spatial and density scales, a multiphase model of the interstellar medium which accounts for the observed scaling relations of molecular clouds, and a supernova-origin model for dust which can explain the existence of dust in cosmologically young objects. By applying ART2 to the hydrodynamic simulations of Li et al., we reproduce the observed spectral energy distribution (SED) and inferred dust properties of SDSS J1148+5251, the most distant Sloan quasar. We find that the dust and infrared emission are closely associated with the formation and evolution of the quasar host. The system evolves from a cold to a warm ultraluminous infrared galaxy (ULIRG) owing to heating and feedback from stars and the active galactic nucleus (AGN). Furthermore, the AGN activity has significant implications for the interpretation of observation of the hosts. Our results suggest that vigorous star formation in merging progenitors is necessary to reproduce the observed dust properties of z ∼ 6 quasars, supporting a merger-driven origin for luminous quasars at high redshifts and the starburst-to-quasar evolutionary hypothesis.