No, it's not unlockable - it just IS. For every certain numbers of "balloons" you get, you get an animal babies statue. I have NO idea of the number (never kept count), but after say, 25, you'll see a wooden "crated animnal" at your front gate. The first time, I didn't know what it was, so I put it in an exhibit and uncrated it. Then, I discovered it was the statue.
Just so you know, the statues do NOT come in "animal" crates. The crates are large, and very light colored wooden boxes, with no air holes, so there's no mistaking them for animals, although the 'mouse tip' SAYS "crated animal", it's really a statue.
So - keep breeding those endangered babies! :lol