Density functional theory (DFT) is widely used to study defects in monolayer graphene with a view to applications ranging from water filtration to electronics to investigations of radiation damage in graphite moderators. To assess the accuracy of DFT in such applications, we report diffusion quantum Monte Carlo (DMC) calculations of the formation energies of some common and important point defects in monolayer graphene: monovacancies, Stone-Wales defects, and silicon substitutions. We find that standard DFT methods underestimate monovacancy formation energies by around 1 eV. The disagreement between DFT and DMC is somewhat smaller for Stone-Wales defects and silicon substitutions. We examine vibrational contributions to the free energies of formation for these defects, finding that vibrational effects are non-negligible. Finally, we compare the DMC atomization energies of monolayer graphene, monolayer silicene, and bulk silicon, finding that bulk silicon is significantly more stable than monolayer silicene by 0.7522(5) eV per atom.