There are many important applications for detecting and localizing specific sound events within long, untrimmed documents including keyword spotting, medical observation, and bioacoustic monitoring for conservation. Deep learning techniques often set the state-of-the-art for these tasks. However, for some types of events, there is insufficient labeled data to train deep learning models. In this paper, we propose novel approaches to few-shot sound event detection utilizing region proposals and the Perceiver architecture, which is capable of accurately localizing sound events with very few examples of each class of interest. Motivated by a lack of suitable benchmark datasets for few-shot audio event detection, we generate and evaluate on two novel episodic rare sound event datasets: one using clips of celebrity speech as the sound event, and the other using environmental sounds. Our highest performing proposed few-shot approaches achieve 0.575 and 0.672 F1-score, respectively, with 5-shot 5-way tasks on these two datasets. These represent absolute improvements of 0.200 and 0.234 over strong proposal-free few-shot sound event detection baselines.