We explore structural, electronic, and magnetic properties of two-dimensional (2D) gallium nitride (GaN) monolayer (ML) doped with different elements belonging to the groups III–VI, using density functional theory (DFT) with the Perdew–Burke–Ernzerhof (PBE) functional and the screened hybrid functional (HSE06) approaches as well as molecular dynamics (MD) simulations. Dopant interactions in Ga- and N-rich environments are investigated by varying their concentrations from 1.38 to 5.5%. Our calculations reveal that oxygen and aluminum impurities are the most preferred candidates under Ga- and N-rich conditions, respectively. The electronic structure studies indicate that dopants containing an even number of valence electrons introduce magnetic behavior with spin-polarized properties, or n-type conductivity with nonmagnetic features, depending on the stoichiometric III/V ratio during growth. Dopants with an odd number of valence electrons modify the GaN ML band structure from indirect to direct bandgap at the Γ point, depending on dopant types at different III/V ratios as well as substitutional site. The calculated charge transfer explains the dopants’ influence on the band structure and bond nature. The HSE calculations of doped g-GaN MLs show a 0.23–1.48 eV increase in the band gaps including the spin-polarized band structures when compared with their PBE values. MD calculations suggest high structural stability at high growth temperatures. Such dopant-induced modifications in structural and physical properties of 2D GaN ML could potentially allow use of this material in diverse electronic, optoelectronic, and spintronic applications.