Yes, there are several anime that feature animal characters as the main focus of the story, often with little to no human presence. Here are a few examples:
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"BNA: Brand New Animal" - While it features humanoid animals, the story revolves around a society of anthropomorphic animals, with the main character being a human who transforms into a tanuki.
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"Kemono Friends" - This series features anthropomorphized animal characters in a safari park-like environment, where each character represents a different animal species.
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"Aggretsuko" - Although it features a mix of human and anthropomorphic characters, the focus is on animal characters navigating work and life.
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"Bananya" - A short series about a cat who is also a banana. Each episode features the daily adventures of these cute characters.
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"A Little Snow Fairy Sugar" - While more focused on fantastical creatures, it contains elements of anthropomorphism.
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"Ginga Nagareboshi Gin" - This classic series follows a group of dogs on their quest to battle a monstrous bear.
While some of these may not align perfectly with your request for "just animal characters," they offer a similar feel. If you're looking for a more pure representation of animal life akin to "Leafie," you might find animated films or shows that aren’t strictly anime but explore animal stories in depth.