Epitaxially-grown semiconductor quantum dots (QDs) provide an attractive platform for the development of deterministic sources of high-quality quantum states of light. Such non-classical light sources are essential for quantum information processing and quantum communication. QDs emitting in the telecom wavelengths are especially important for ensuring compatibility with optical fiber systems required to implement quantum communication networks. To this end, GaSb QDs fabricated by filling local-droplet etched nanoholes are emerging as a viable approach, yet the electronic properties of such nanostructures have not been studied in detail. In this article, an insight into the electronic structure and carrier dynamics in GaSb/AlGaSb QDs is provided through a systematic experimental analysis of their temperature-dependent photoluminescence behavior. A steady-state rate equation model is used to reveal the relevant energy barriers for thermally activated carrier capture and escape processes. Furthermore, results of detailed theoretical simulations of quantum-confined energy states using the multi-band k·p model and the effective mass method are presented. The purpose of the simulations is to reveal the direct and indirect energy states, carrier wavefunctions, and allowed optical transitions for GaSb QDs with different physical dimensions.