Recently deep learning has dominated many machine learning areas, including spoken language understanding (SLU). However, deep-learning models are notorious for being data-hungry, and the heavily optimized models are usually sensitive to the quality of the training examples provided and the consistency between training and inference conditions. To improve the performance of SLU models on tasks with noise and low training resources, we propose a new SLU benchmarking task: few-shot robust SLU, where SLU comprises two core problems, intent classification (IC) and slot labeling (SL). We establish the task by defining few-show splits on three public IC/SL datasets, ATIS, SNIPS, and TOP, and adding two types of natural noises (adaptation example missing/replacing and modality mismatch) to the splits. We further propose a novel noise-robust few-shot SLU model based on prototypical networks. We show the model consistently outperforms the conventional fine-tuning baseline and another popular meta-learning method, Model-Agnostic Meta-Learning (MAML), in terms of achieving better IC accuracy and SL F1, and yielding smaller performance variation when noises are present.