Quantum key distribution (QKD) is a fundamental functionality of quantum networks. Extending its range requires quantum repeaters, a technology still under development and not yet demonstrated in combination with quantum cryptographic protocols. Here, we address the elementary operation of a viable quantum repeater scheme by evaluating whether correlated photons distributed via entanglement swapping can support secret key distribution. We employ a state-of-the-art deterministic photon source based on a strain-tuned GaAs quantum dot embedded in a photonic cavity and implement a source-independent QKD protocol between two nodes using entanglement-swapped photons. We benchmark the system and present how high-resolution temporal post-selection can enable secure key exchange, with further rate improvements expected through realistic device and protocol optimizations. Due to its compatibility with a wide range of quantum memory platforms, our approach represents a significant step toward long-distance quantum-safe communication.