In this paper, we study band-to-band and intersubband (ISB) characteristics of Si- and Ge-doped GaN/AlN heterostructures (planar and nanowires) structurally designed to absorb in the short-wavelength infrared region, particularly at 1.55 μm. Regarding the band-to-band properties, we discuss the variation of the screening of the internal electric field by free carriers, as a function of the doping density and well/nanodisk size. We observe that nanowire heterostructures consistently present longer photoluminescence decay times than their planar counterparts, which supports the existence of an in-plane piezoelectric field associated to the shear component of the strain tensor in the nanowire geometry. Regarding the ISB characteristics, we report absorption covering 1.45-1.75 μm using Ge-doped quantum wells, with comparable performance to Si-doped planar heterostructures. We also report similar ISB absorption in Si- and Ge-doped nanowire heterostructures indicating that the choice of dopant is not an intrinsic barrier for observing ISB phenomena. The spectral shift of the ISB absorption as a function of the doping concentration due to many body effects confirms that Si and Ge efficiently dope GaN/AlN nanowire heterostructures.