In the cuprate superconductor YBa2Cu3O6+x, hole doping in the CuO2 layers is controlled by both oxygen content and the degree of oxygen ordering. At the composition YBa2Cu3O6.35, the ordering can occur at room temperature, thereby tuning the hole doping so that the superconducting critical temperature gradually rises from 0 to 20 K. Here we exploit this to study the c-axis penetration depth as a function of temperature and doping. The temperature dependence shows the d-wave superconductor surviving to very low doping, with no sign of another ordered phase interfering with the nodal quasiparticles. The only apparent doping dependence is a smooth decline of superfluid density as T(c) decreases.