Remotely doped In0.35Ga0.65As layers of different coverages 6, 9, 11, and 13 ML were grown by molecular beam epitaxy on (100) GaAs. Quantum dot (QD) nucleation was observed in situ by reflection high-energy electron diffraction at 8 ML growth of In0.35Ga0.65As, while for 6 ML, only two-dimensional (2D) growth was observed. Atomic force microscopy, low temperature photoluminescence, and Hall effect measurements confirmed this transition from 2D to three-dimensional growth. Low-frequency noise studies have been performed to probe defects in such heterostructures throughout the transition from a highly strained quantum well to QDs. Results were compared to a bulk n-type GaAs reference sample. We revealed three main defects in GaAs with activation energies of 0.8, 0.54, and 0.35 eV. These defects with the same activation energies were found in all samples. However, structures containing In0.35Ga0.65As QDs show an additional peak at low temperatures due to the presence of defects which are not observed for reference GaAs and quantum well samples. Detailed analysis shows that for 9 and 11 ML In0.35Ga0.65As QD samples this peak corresponds to the well known M1 defect in GaAs with an activation energy of 0.18 eV, while for a coverage of 13 ML the defect was found to have an activation energy of 0.12 eV. All defects were characterized quantitatively in terms of their activation energy, capture cross section, and density. These studies indicate that noise spectroscopy is a very sensitive tool for electronic material characterization on the nanoscale.