It is possible in the same way that it is possible for a human to set foot on another planet - you would have to put the animal in a spaceship and send the spaceship to the planet. Once the spaceship landed, the animal could walk around on the planet if the planet's atmosphere was good for the animal. Otherwise the animal would have to wear a protective suit with air tanks so that it could breathe. Just like a human.

It is, and it has happened. Humans are animals, and humans have set foot on the Moon (which isn't a planet per se, but it is a world, and there is no reason why humans could not set foot on any other planet). There are no planets in the known universe save Earth that can support animal life without protection (in this case, a space suit). The search for other Earth-like planets in the universe is still underway.