Achieving pure single-photon emission is essential for a range of quantum technologies, from optical quantum computing to quantum key distribution to quantum metrology. Among solid-state quantum emitters, colloidal lead halide perovskite (LHP) nanocrystals (NCs) have garnered significant attention due to their interesting structural and optical properties, which make them appealing single-photon sources (SPSs). However, their practical utilization for quantum technology applications has been hampered by environment-induced instabilities. In this study, we fabricate and characterize in a systematic manner Zn-treated $CsPbBr_3$ colloidal NCs obtained through $Zn^{2+}$ ion doping at the Pb-site, demonstrating improved stability under dilution and illumination. These doped NCs exhibit high single-photon purity, reduced blinking on a sub-millisecond timescale and stability of the bright state for excitation powers well above the saturation levels. Our findings highlight the potential of this synthesis approach to optimize the performance of LHP-based SPSs, opening up interesting prospects for their integration into nanophotonic systems for quantum technology applications.