Effective and controllable doping is instrumental for enabling the use of III-V semiconductor nanowires (NWs) in practical electronics and optoelectronics applications. To this end, dopants are incorporated during self-catalyzed growth via vapor-liquid-solid mechanism through the catalyst droplet or by vapor-solid mechanism of the sidewall growth. The interplay of these mechanisms together with the competition between axial elongation and radial growth of NWs can result in dopant concentration gradients along the NW axis. Here, we report an investigation of Be-doped p-type GaAs NWs grown by the self-catalyzed method on lithography-free Si/SiO x templates. The influence of dopant incorporation on the structural properties of the NWs is analyzed by scanning and transmission electron microscopy. By combining spatially resolved Raman spectroscopy and transport characterization, we are able to estimate the carrier concentration, mobility and resistivity on single-NW level. We show that Be dopants are incorporated predominantly by vapor-solid mechanism for low Be flux, while the relative contribution of vapor-liquid-solid incorporation is increased for higher Be flux, resulting in axial dopant gradients that depend on the nominal doping level.