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As the power grid becomes more complex and dynamic, accurate short-term load forecasting (STLF) with probabilistic information is a prerequisite for various smart grid applications. For doing this, various deep learning models have been proposed, and recent models increase model size and complexity to achieve better accuracy which could also increase the burden on model design, computation time, and resources. To this end, we propose a novel deep learning model for accurate and efficient probabilistic STLF (PSTLF). First, we develop an STLF model utilizing the multi-layer perceptron (MLP)-mixer structure, i.e., MLP-mixer for STLF (MM-STLF), that has an advantage in forecasting accuracy and efficiency compared to the other deep learning models. Then, we propose a random quantile regression (RQR) method that takes a cumulative probability $\tau $ as an input to the model and is trained on random $\tau \text{s}$ . By combining MM-STLF and RQR, we develop a novel deep-PSTLF model, namely quantile-mixer (Q-mixer). We evaluate the overall performance of the proposed model with seven load datasets in terms of prediction error, model size, and inference time, respectively. Through experiments, various STLF models and probabilistic forecasting methods are compared, and the experimental results demonstrate the effectiveness of Q-mixer in load forecasting.