Nuclear quantum effects (NQEs) cause the nuclei of light elements like hydrogen to delocalize, affecting numerous properties of water and aqueous solutions, such as hydrogen-bonding and proton transfer barriers. Here, we address the prototypical case of aqueous NaOH solutions by investigating the effects of quantum nuclear fluctuations on radial distribution functions, hydrogen-bonding geometries, power spectra, proton transfer barriers, proton transfer rates, water self-exchange rates around the Na+ cations, and diffusion coefficients, for the full room-temperature solubility range. These properties were calculated from classical and ring polymer molecular dynamics simulations employing a reactive high-dimensional neural network potential based on dispersion-corrected density functional theory reference calculations. We find that NQEs have a very small impact on the solvation structure around Na+, slightly strengthen the water-water and water-hydroxide hydrogen bonds, and lower the peak positions in the power spectra for the HOH bending and OH stretching modes by about 50 and 100 cm(-1), respectively. Moreover, NQEs significantly lower the proton transfer barriers, thus increasing the proton transfer rates, resulting in an increase of the diffusion coefficient in particular of OH-, as well as a decrease of the mean residence time of molecules in the first hydration shell around Na+ at high NaOH concentrations.