We report measurements of picosecond dynamics of individual nickel nanomagnets as a function of magnet dimension, aspect ratio, and magnetic environment. Spatial sensitivity to nanomagnet diameters as small as 125 nm is achieved by use of cavity enhancement of the magneto-optic Kerr effect (CE-MOKE). The importance of single-particle measurements without ensemble effects for extracting the size dependence of the intrinsic nanomagnet material properties is demonstrated.