The Channel Quality Indicator (CQI) is a fundamental component of channel state information (CSI) that enables adaptive modulation and coding by selecting the optimal modulation and coding scheme to meet a target block error rate. While AI-enabled CSI feedback has achieved significant advances, especially in precoding matrix index feedback, AI-based CQI feedback remains underexplored. Conventional subband-based CQI approaches, due to coarse granularity, often fail to capture fine frequency-selective variations and thus lead to suboptimal resource allocation. In this paper, we propose an AI-driven subcarrier-level CQI feedback framework tailored for 6G and NextG systems. First, we introduce CQInet, an autoencoder-based scheme that compresses per-subcarrier CQI at the user equipment and reconstructs it at the base station, significantly reducing feedback overhead without compromising CQI accuracy. Simulation results show that CQInet increases the effective data rate by 7.6% relative to traditional subband CQI under equivalent feedback overhead. Building on this, we develop SR-CQInet, which leverages super-resolution to infer fine-grained subcarrier CQI from sparsely reported CSI reference signals (CSI-RS). SR-CQInet reduces CSI-RS overhead to 3.5% of CQInet's requirements while maintaining comparable throughput. These results demonstrate that AI-driven subcarrier-level CQI feedback can substantially enhance spectral efficiency and reliability in future wireless networks.