Integrated Vehicular Networks (IVNs) require the exchange of large volumes of safety-critical broadcast messages, where ensuring message origin authenticity and data integrity can be more critical than message confidentiality. Many existing authenticated broadcast mechanisms either rely on classical public-key cryptographic techniques that are vulnerable to quantum adversaries or suffer from significant verification and revocation overhead under dense traffic conditions. This paper proposes QS-BTrust, a quantum-secure and privacy-preserving authenticated broadcast protocol that combines Physical Unclonable Functions (PUFs), post-quantum digital signatures, and Hashgraph-based authentication tag management. QS-BTrust enables immediate message authentication with constant-time verification complexity, supports pseudo-indistinguishable identities to achieve unlinkability, and enables revocation without introducing additional message overhead, even in dense traffic scenarios. The security of QS-BTrust is analyzed under the Dolev–Yao (DY) adversary model to establish protocol-level robustness against active network attacks and is formally validated using ProVerif to verify broadcast authenticity and resistance to message forgery. The protocol is further analyzed under both the Random Oracle Model (ROM) and the Quantum Random Oracle Model (QROM), demonstrating robustness against replay, impersonation, message forgery, Sybil, and quantum-assisted attacks. Security guarantees are evaluated using adversarial success probability, unforgeability, and impersonation advantage as attack metrics. Simulation-based performance evaluation further shows that QS-BTrust achieves lower verification overhead under high message loads compared to representative broadcast authentication schemes, while providing quantum resistance. These characteristics make QS-BTrust well suited for large-scale and critical vehicular communication environments.