We explore the use of knowledge distillation (KD) for learning compact and accurate models that enable classification of animal behavior from accelerometry data on wearable devices. To this end, we take a deep and complex convolutional neural network, known as residual neural network (ResNet), as the teacher model. ResNet is specifically designed for multivariate time-series classification. We use ResNet to distil the knowledge of animal behavior classification datasets into soft labels, which consist of the predicted pseudo-probabilities of every class for each datapoint. We then use the soft labels to train our significantly less complex student models, which are based on the gated recurrent unit (GRU) and multilayer perceptron (MLP). The evaluation results using two real-world animal behavior classification datasets show that the classification accuracy of the student GRU-MLP models improves appreciably through KD, approaching that of the teacher ResNet model. To further reduce the computational and memory requirements of performing inference using the student models trained via KD, we utilize dynamic fixed-point quantization through an appropriate modification of the computational graphs of the models. We implement both unquantized and quantized versions of the developed KD-based models on the embedded systems of our purpose-built collar and ear tag devices to classify animal behavior in situ and in real time. The results corroborate the effectiveness of KD and quantization in improving the inference performance in terms of both classification accuracy and computational and memory efficiency.