The pairwise kinematic Sunyaev-Zeldovich (kSZ) signal from galaxy clusters is a probe of their line-of-sight momenta, and thus a potentially valuable source of cosmological information. In addition to the momenta, the amplitude of the measured signal depends on the properties of the intra-cluster gas and observational limitations such as errors in determining cluster centers and redshifts. In this work we simulate the pairwise kSZ signal of clusters at z<1, using the output from a cosmological N-body simulation and including the properties of the intra-cluster gas via a model that can be varied in post-processing. We find that modifications to the gas profile due to star formation and feedback reduce the pairwise kSZ amplitude of clusters by ~50%, relative to the naive gas traces mass assumption. We demonstrate that mis-centering can reduce the overall amplitude of the pairwise kSZ signal by up to 10%, while redshift errors can lead to an almost complete suppression of the signal at small separations. We confirm that a high-significance detection is expected from the combination of data from current-generation, high-resolution CMB experiments, such as the South Pole Telescope, and cluster samples from optical photometric surveys, such as the Dark Energy Survey. Furthermore, we forecast that future experiments such as Advanced ACTPol in conjunction with data from the Dark Energy Spectroscopic Instrument will yield detection significances of at least 20{sigma}, and up to 57{sigma} in an optimistic scenario. Our simulated maps are publicly available at: http://www.hep.anl.gov/cosmology/ksz.html