Molecular p-doping of the conjugated polymer poly(3-hexylthiophene) (P3HT) with 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ) is a widely studied model system. Underlying structure-property relationships are poorly understood because processing and doping are often carried out simultaneously. Here, we exploit doping from the vapor phase, which allows us to disentangle the influence of processing and doping. Through this approach, we are able to establish how the electrical conductivity varies with regard to a series of predefined structural parameters. We demonstrate that improving the degree of solid-state order, which we control through the choice of processing solvent and regioregularity, strongly increases the electrical conductivity. As a result, we achieve a value of up to 12.7 S cm-1 for P3HT:F4TCNQ. We determine the F4TCNQ anion concentration and find that the number of (bound + mobile) charge carriers of about 10-4 mol cm-3 is not influenced by the degree of solid-state order. Thus, the observed increase in electrical conductivity by almost 2 orders of magnitude can be attributed to an increase in charge-carrier mobility to more than 10-1 cm2 V-1 s-1. Surprisingly, in contrast to charge transport in undoped P3HT, we find that the molecular weight of the polymer does not strongly influence the electrical conductivity, which highlights the need for studies that elucidate structure-property relationships of strongly doped conjugated polymers.