Internet of Things (IoT) devices are expected to operate in environments where the available power is dynamic and uncertain. This leads to a stark security vs. energy consumption trade-off in post-quantum cryptography. While modern post-quantum cryptographic (PQC) primitives like ML-KEM (Kyber-512) provide strong quantum-secure security, they are computationally expensive and require large amounts of energy. In this paper, an energy-aware key management protocol Crypto-Agile Key Exchange, CAKE is proposed. CAKE is evaluated using a simulation framework targeted to a Cortex-M4 based IoT node that operates under realistics solar energy harvesting settings. Our results demonstrate that proposed protocol achieves zero session drops at the node for up to 10,000 state transitions and it achieves a reduction of 47.3% in number of Kyber KEM operations in indoor settings, while it achieves an average transition time of 14.7 ms. Under constrained conditions, the proposed protocol is proven to be IND-CCA2 secure in the high-energy state, and 128-bit classical security is preserved in the low-energy state.