Motivation: To address unmet needs for accurate, rapid, and high-fidelity quantitative MRI using a 3D-QALAS sequence. Goal(s): To enable accurate T1 and T2 mapping with reduced biases, g-factor noise amplification, and relaxation-related blurring compared to conventional QALAS. Approach: We employed a zero-shot self-supervised subspace reconstruction technique, Zero-DeepSub, which combines scan-specific deep-learning-based reconstruction with low-rank subspace modeling, and demonstrated the performance using ISMRM/NIST phantom and pediatric patients. Results: Zero-DeepSub enabled a highly accelerated, 2 min acquisition at 1 mm isotropic resolution at 3T, as well as a 5 min pediatric exam at 1.2 mm isotropic resolution at 1.5T. Impact: Zero-DeepSub enabled accurate T1 and T2 mapping with reduced biases, g-factor noise amplification, and relaxation-related blurring, showing the potential to substantially speed up pediatric brain exams, thus obviating the need for or reducing the amount of sedation and anesthesia.