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Using the one-dimensional Hubbard model, which is commonly used for describing, e.g., high-$T_c$ superconducting cuprates, we study high-harmonic generation (HHG) from doped, correlated materials. Doping is modeled by changing the number of electrons in the lattice from the conventional half-filling case. For relatively small Hubbard $U$, i.e., small electron-electron correlation, we find little to no effect of doping on the dynamics and the HHG spectra. For increasing $U$ the degree of doping has a marked effect on the dynamics and spectra. We explain these findings through the quasiparticle-based doublon-holon picture. The dynamics are separated into two types, firstly doublon and holon movement, and, secondly, doublon-holon pair creation and annihilation. Doping results in all configurations containing doublons or holons. Those quasiparticles can move at no extra cost in energy regardless of the correlation level. This motion at no energy cost increases the high-harmonic gain for low and medium harmonic orders. We discuss that in the high-$U$ limit, antiferromagnetic ordering becomes increasingly unlikely with increasing doping rates and explain an associated drop in the high-order harmonics relative to the case of half filling.