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Cadmium Arsenide (Cd₃As₂) is a prototypical Dirac semimetal that manifests topological properties in a 3D bulk material. In defect-free Cd₃As₂, the Fermi level E_F lies at a minimum in the density of states at the Dirac point, but experimentally it forms with excess electron carriers and an elevated E_F, thereby masking the topological features. To computationally study the self-doping of Cd₃As₂, we combine density functional theory (DFT) calculations for defect formation energies with quasi-particle self-consistent GW (QSGW) electronic structure calculations. We demonstrate an innate dependence of the point defect formation energies on carrier concentrations and use the QSGW calculated density of states to extrapolate formation energies to arbitrary electron concentrations. This approach allows the quantitative modeling of thermodynamic defect equilibria in topological semimetals and is used to predict how Cd₃As₂ growth conditions affect the position of E_F relative to the Dirac point.