There is animal called the red fox. They are a canine - related to the dogs we keep as pets today - and have a soft red hue to their fur. It is one of the true fox breeds - meaning that the foxes that it’s related to form a true group of animals that have split off from each other. It’s also one of the largest of the true foxes. However, there are other animals that are red.
The red panda, for instance, is a red animal. Quite a few bird species are red. They include the scarlet tanager, the cardinal, and even the purple finch as it has more pinkish-red to its color than blue. One rather famous red bird is the scarlet ibis, for which the short story was named.