Regardless of several investigations to elucidate the ground state of the strongly correlated electron systems in doped Mott-insulators (MIs), the origin of the doping-induced insulator-to-metal transition (IMT) remains a crucial and debatable subject in solid-state physics. Herein, we explore the consequences of Re/Ir-doping at the Os-site (Re/Ir@Os), on the physical properties of the MI ferrimagnetic (FiM) Ca2FeOsO6 double perovskite oxides using density functional theory calculations. The doped structures' solidity is analyzed by computing the defect formation energies in terms of the dopant-rich situation, which confirms their growth credibility at ambient conditions along with mechanical and dynamical stabilities. Various FiM spin-ordering is taken into account in the doped structures to analyze the magnetic ground state, which is FiM-I/FiM-II in the Re/Ir@Os-doped system. Remarkably, an IMT is predicted in the Re/Ir@Os-doped structures, which is due to the admixture of the partially occupied 5d orbitals of these ions. The calculated partial spin magnetic moments (ms) of +4.12, -1.58, -0.75 and +0.88μB on the Fe, Os, Re, and Ir ions, endorse the +3, +5, +5, and +4 states having electronic configurations of t32g↑t02g↓e2g↑e0g↓, t32g↑t02g↓e0g↑e0g↓, t22g↑t02g↓e0g↑e0g↓, t32g↑t22g↓e0g↑e0g↓, respectively. The "+" and "-" signs on the ions ms values, lead the systems into various FiM magnetic ordering. Moreover, the estimated Curie temperature (TC) using the Heisenberg model in the pristine structure is 334 K, which is close to the experimentally observed value of 320 K along with a colossal uniaxial magneto crystalline anisotropy energy constant (K) of 2.95 × 107 erg cm-3 having the easy magnetic axis of the ac-plane ([101]). It is established that TC/K reduces and enhances to 298 K/1.33 × 107 erg cm-3 and 365 K/4.71 × 107 erg cm-3 for the Re@Os and Ir@Os-doped motif due to an increase and decrease in the octahedral distortions compared to that of the pristine system, respectively.