Abstract: CAN XL supports payloads of up to 2048 bytes per frame. CANsec adds a MACsec-like data plane but leaves key agreement unspecified. Pre-shared keys alone provide no forward secrecy, and classical elliptic-curve exchange is vulnerable to cryptographically relevant quantum computers, a concern for long-lived vehicles. This paper proposes PQ-CKA, a CANsec key agreement based on ML-KEM (FIPS 203): the server broadcasts an ephemeral encapsulation key, members return ciphertexts authenticated with pre-shared keys, and the secure association key is distributed under KEM-derived key-encryption keys. A compositional worst-case time-to-key (WC-TTK) bound accounts for CAN XL frame durations, arbitration with transmission errors, first-in-first-out server processing and execution times derived from measured Cortex-M4 cycle counts. Evaluation uses a real-vehicle message set with 106 identifiers and 2,392 frames/s at 50% bus load, with 10 000-run simulations checking the bound. For 16 ECUs, ML-KEM-768 gives a WC-TTK of 122.7 ms versus 119.4 ms for X25519; all members hold the new key after 94.1 ms. The same protocol requires 363.5 ms on CAN FD at 2 Mbit/s. Mutual ML-DSA authentication increases the bound to 337.3 ms and makes it probabilistic because signing has an unbounded geometric tail. Sequential protocol rounds and the server's decapsulation rate dominate time-to-key, rather than post-quantum message size.