Recognizing animal activities holds a crucial role in monitoring animals' health and well-being. Additionally, a considerable audience is keen on monitoring their pets' well-being and health status. Insight into animals' habitual activities and patterns not only aids veterinarians in accurate diagnoses but also offers pet owners early alerts. Traditional methods of tracking animal behavior involve wearable sensors like IMU sensors, collars, or cameras. Nevertheless, concerns, including privacy, robustness, and animal discomfort persist. In this study, radar technology, a noninvasive remote sensing technology widely employed in human health monitoring, is explored for AAR. Radar enables fine motion analysis through Microdoppler spectrograms. Utilizing an off-the-shelf FMCW mm-wave radar, we gather data from five distinct activities and postures. Merging radar technology with Machine Learning and Deep Learning algorithms helps distinguish diverse pet activities and postures. Specific challenges in AAR, such as random movements, being uncontrollable, noise, and small animal size, make radar adoption for animal monitoring complex. In this study, RayPet unveils different challenges and solutions regarding monitoring small animals. To overcome the challenges, different signal processing steps are devised and implemented, tailored for animals. We use four types of classifiers and achieve an accuracy rate of 89%. This progress marks an important step in using radar technology to observe and comprehend activities and postures in pets in particular and in animals in general, contributing to our knowledge of animal well-being and behavior analysis.