Query cost estimation is a classical task for database management. Recently, researchers have applied AI-driven methods to implement query cost estimation for achieving high accuracy. However, two defects of the feature design lead to poor time-accuracy efficiency in the query cost estimation task. On the one hand, existing works only encode the query plan and data statistics while ignoring some important variables, like storage structure, hardware, database knobs, etc. These variables also have a significant impact on the query cost. On the other hand, existing works suffer the heavy model training and model inference due to inefficient features, such as the index encoding of write-only workloads. To address the above two problems, we first propose an efficient feature engineering for query cost estimation, called QCFE, consisting of the feature snapshot and feature reduction algorithm. (1) We design a novel concept called feature snapshot to efficiently integrate the influences of the missing variables. (2) We propose a difference-propagation feature reduction method for query cost estimation to filter the ineffective features. Compared to state-of-the-art methods, QCFE demonstrates significant improvements in various aspects with well-known benchmarks. QCFE saves up to 50% time consumption for model training, resulting in more efficient and faster training processes. QCFE also optimizes the mean q-error by 19.8% in TPCH, leading to more precise query cost estimation. QCFE offers up to an impressive 8 times inference speedup in query inference throughput.