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The emergence of fault-tolerant quantum computing poses an existential threat to classical public-key cryptographic systems, including RSA and Elliptic Curve Cryptography (ECC), through Shor's polynomial-time factorization algorithm. The Harvest Now, Decrypt Later (HNDL) attack paradigm further amplifies this threat by enabling adversaries to archive ciphertext today for future quantum-enabled decryption, rendering long-term data confidentiality immediately at risk. While the National Institute of Standards and Technology (NIST) finalized post-quantum cryptographic standards ML-KEM (FIPS 203) and ML-DSA (FIPS 204) in August 2024, their practical integration into complete application-level communication systems remains a largely unaddressed research gap. This paper presents QuantumShield, a hybrid post-quantum secure peer-to-peer communication platform that integrates ML-KEM-768 for quantum-safe key encapsulation, ML-DSA-65 for authenticated digital signatures, and AES-256-GCM for high-throughput symmetric encryption. Our primary research contribution is a rigorous empirical analysis of PQC integration overhead in a real-world communication pipeline, quantifying latency, key size, and security trade-offs against classical RSA-2048 and ECC-256 baselines under controlled experimental conditions. Experimental evaluation across 1,000 iterations demonstrates that ML-KEM-768 encapsulation completes in 2.8 ± 0.2 ms compared to 4.1 ± 0.3 ms for ECDH key agreement — a 32% latency reduction while providing NIST Level 3 post-quantum security. The complete secure transfer pipeline processes 1 MB files in under 22 ms on commodity hardware. The system further provides interactive cryptographic visualization, adversary threat modeling, tamper detection simulation, and a hybrid migration framework demonstrating practical transition from classical to post-quantum infrastructure. QuantumShield establishes that quantum-safe communication is not merely theoretical but deployable today with negligible performance compromise.