We study quasar clustering on small scales, modeling clustering amplitudes using halo-driven dark matter descriptions. From 91 pairs on scales <35 h-1 kpc, we detect only a slight excess in quasar clustering over our best-fit large-scale model. Integrated across all redshifts, the implied quasar bias is bQ = 4.21 ± 0.98 (bQ = 3.93 ± 0.71) at ~18 h-1 kpc (~28 h-1 kpc). Our best-fit (real space) power index is ~-2 [i.e., ξ(r) vprop r-2], implying steeper halo profiles than currently found in simulations. Alternatively, quasar binaries with separation <35 h-1 kpc may trace merging galaxies, with typical dynamical merger times td ~ (610 ± 260)m-1/2 h-1 Myr, for quasars of host halo mass m × 1012 h-1 M☉. We find that UV-excess quasars at ~28 h-1 kpc cluster >5 times higher at z > 2 than at z < 2, at the 2.0 σ level. However, as the space density of quasars declines as z increases, an excess of quasar binaries (over expectation) at z > 2 could be consistent with reduced merger rates at z > 2 for the galaxies forming UV-excess quasars. Comparing our clustering at ~28 h-1 kpc to a ξ(r) = (r/4.8 h-1 Mpc)-1.53 power law, we find an upper limit on any excess of a factor of 4.3 ± 1.3, which, noting some caveats, differs from large excesses recently measured for binary quasars, at 2.2 σ. We speculate that binary quasar surveys that are biased to z > 2 may find inflated clustering excesses when compared to models fit at z < 2. We provide details of 111 photometrically classified quasar pairs with separations <0.1'. Spectroscopy of these pairs could significantly constrain quasar dynamics in merging galaxies.