Mission critical (MC) applications such as defense operations, energy management, cybersecurity, and aerospace control require reliable, deterministic, and low-latency decision making under uncertainty. Although the classical Artificial Intelligence (AI) approaches are effective, they often struggle to meet the stringent constraints of robustness, timing, explainability, and safety in the MC domains. Quantum Artificial Intelligence (QAI), the fusion of artificial intelligence and quantum computing (QC), can potentially provide transformative solutions to the challenges faced by classical ML models. QAI is a broader umbrella than Quantum Machine Learning (QML) and additionally includes quantum optimization, search, and reasoning; we use QAI throughout the paper for the field at large, and QML only for learning-specific subroutines. The principal contributions of this work are: (i) a systematic survey of QAI methods analyzed through the lens of MC requirements like certification, robustness, and timing; (ii) a conceptual quantum cloud resource management and scheduling framework with deployment assumptions, complexity analysis, and failure-mode discussion; and (iii) an identification of the gaps between current QAI capabilities and MC systems requirements. We also propose a conceptual model for management of quantum resources and scheduling of applications driven by timeliness constraints. We discuss multiple challenges, including trainability limits, data access, and loading bottlenecks, verification of quantum components, and adversarial QAI. Finally, we outline future research directions toward achieving interpretable, scalable, and hardware-feasible QAI models for MC application deployment.