pet lost and found system

Hello.

I don't think Amazon Rekognition currently has a function that directly identifies animal faces.
https://docs.aws.amazon.com/rekognition/latest/dg/what-is.html

Therefore, I think you will need a mechanism to create a custom label like the one in the AWS blog below to identify it as an animal.
If we can do this, we believe it will be possible to identify images of similar animals.
https://aws.amazon.com/jp/blogs/machine-learning/training-a-custom-single-class-object-detection-model-with-amazon-rekognition-custom-labels/
https://aws.amazon.com/jp/blogs/aws/amazon-rekognition-image-detection-and-recognition-powered-by-deep-learning/