You can absolutely make it anything. It's your story, your ideas. You can go with real currency. Are they talking animals? I would assume so, and as intelligent as you want them. Maybe if you were going more organic, I would go with some kind of valuable nut, or food? Are they bartering and trading? If you had it high tech, you can invent something completely new? Or jewels, gems? Nuggets of gold?
It's what fits for your story. If it's a fantasy, you have an endless amount of ideas. But if you were trying to make the animals realistic, the coins or paper currency would work too.