Combining cosmological SPH simulations with a previously developed Lyman Alpha production/transmission model and the Early Reionization Model (ERM, reionization ends at redshift z~7), we obtain Lyman Alpha and UV Luminosity Functions (LFs) for Lyman Alpha Emitters (LAEs) for redshifts between 5.7 and 7.6. Matching model results to observations at z~5.7 requires escape fractions of Lyman Alpha, f_alpha=0.3, and UV (non-ionizing) continuum photons, f_c=0.22, corresponding to a color excess, E(B-V)=0.15. We find that (i) f_c increases towards higher redshifts, due the decreasing mean dust content of galaxies, (ii) the evolution of f_alpha/f_c hints at the dust content of the ISM becoming progressively inhomogeneous/clumped with decreasing redshift. The clustering photoionization boost is important during the initial reionization phases but has little effect on the Lyman Alpha LF for a highly ionized IGM. Halo (stellar) masses are in the range 10.0 < \log M_h < 11.8 (8.1 < \log M_* < 10.4) with M_h \propto M_*^{0.64}. The star formation rates are between 3-120 solar masses per year, mass-weighted mean ages are greater than 20 Myr at all redshifts, while the mean stellar metallicity increases from Z=0.12 to 0.22 solar metallicity from z~7.6 to z~5.7; both age and metallicity positively correlate with stellar mass. The brightest LAEs are all characterized by large star formation rates and intermediate ages (~200 Myr), while objects in the faint end of the Lyman Alpha LF show large age and star formation rate spreads. With no more free parameters, the Spectral Energy Distributions of three LAE at z~5.7 observed by Lai et al. (2007) are well reproduced by an intermediate age (182-220 Myr) stellar population and the above E(B-V) value.