Previous observations of quasar host haloes at z~2 have uncovered large quantities of cool gas that exceed what is found around inactive galaxies of both lower and higher masses. To better understand the source of this excess cool gas, we compiled an exhaustive sample of 195 quasars at z~1 with constraints on chemically enriched, cool gas traced by MgII absorption in background quasar spectra from the Sloan Digital Sky Survey. This quasar sample spans a broad range of luminosities from L_bol_=10^44.4^ to 10^46.8^erg/s and allows an investigation of whether halo gas properties are connected with quasar properties. We find a strong correlation between luminosity and cool gas covering fraction. In particular, low-luminosity quasars exhibit a mean gas covering fraction comparable to inactive galaxies of similar masses, but more luminous quasars exhibit excess cool gas approaching what is reported previously at z~2. Moreover, 30-40 percent of the MgII absorption occurs at radial velocities of |Delta_v_|>300km/s from the quasar, inconsistent with gas bound to a typical quasar host halo. The large velocity offsets and observed luminosity dependence of the cool gas near quasars can be explained if the gas arises from: (1) neighbouring haloes correlated through large-scale structure at Mpc scales, (2) feedback from luminous quasars or (3) debris from the mergers thought to trigger luminous quasars. The first of these scenarios is in tension with the lack of correlation between quasar luminosity and clustering while the latter two make distinct predictions that can be tested with additional observations.