We have used nuclear quadrupole resonance (NQR) to probe microscopically the response of a prototypical quantum critical metal CeCoIn5 to substitutions of small amounts of Cd for In. Approximately half of the Cd substituents induce local Ce moments in their close proximity, as observed by site-dependent longitudinal nuclear spin relaxation rates 1/T1. To reaffirm that localized f moments are induced around the Cd substituents, we find a Gaussian spin-echo decay rate 1/T2G of transverse nuclear spin relaxation. Further, for the NQR subpeak is found to be proportional to temperatures, again indicating local moments fluctuations around the Cd substituents, while that for the NQR main peak shows a T0.7-dependence. The latter temperature dependence is close to 0.75 in pure CeCoIn5 and indicates that the bulk electronic state is located close to a two dimensional quantum critical instability.