Quantum software systems represent a new realm in software engineering, utilizing quantum bits (Qubits) and quantum gates (Qgates) to solve the complex problems more efficiently than classical counterparts. Agile software development approaches are considered to address many inherent challenges in quantum software development, but their effective integration remains unexplored. This study investigates key causes of challenges that could hinders the adoption of traditional agile approaches in quantum software projects and develop an Agile-Quantum Software Project Success Prediction Model (AQSSPM). Firstly, we identified 19 causes of challenging factors discussed in our previous study, which are potentially impacting agile-quantum project success. Secondly, a survey was conducted to collect expert opinions on these causes and applied Genetic Algorithm (GA) with Naive Bayes Classifier (NBC) and Logistic Regression (LR) to develop the AQSSPM. Utilizing GA with NBC, project success probability improved from 53.17 to 99.68%, with cost reductions from 0.463 to 0.403%. Similarly, GA with LR increased success rates from 55.52 to 98.99%, and costs decreased from 0.496 to 0.409% after 100 iterations. Both methods result showed a strong positive correlation (rs = 0.955) in causes ranking, with no significant difference between them (t = 1.195, p = 0.240 > 0.05). The AQSSPM highlights critical focus areas for efficiently and successfully implementing agile-quantum projects considering the cost factor of a particular project.