In this work we study the double ionization yields and kinetic energy spectra of a two-electron spherical quantum dot (QD) exposed in laser fields. The theoretical description is based on an ab initio nonperturbative configuration interaction theory capable of describing the two-electron QD dynamics in THz and mid-IR ultrashort laser fields. The QD's confinement potential is approximated to have a Gaussian-like spatial dependence. We have found that significant variations of the two-electron kinetic energy patterns and two-photon double ionization yields occur as we vary the QD's size. For a given laser pulse, the double ionization yield increases by orders of magnitude when the dot size is reduced. The size of the QD determines the sequential or direct character of the two-photon double ionization process. Provided that it is energetically allowed, the sequential two-photon double ionization process, requiring minimal interelectronic correlations, becomes dominant over the direct one. In the sequential regime, the corresponding two-electron kinetic energy spectrum changes from a broadened single-peaked to a doubly peaked one. Moreover, we also have identified features in the spectrum that are distinctively different than those in its atomic counterpart.