All levity aside, we can see here an image of three fellas riding ostriches. Here we can see a dude riding a Zebra. This begs the following questions:
I don't know that any evidence exists to show why Hannibal DIDNT bring those animals, but he would have no reason to. Horses were great for warfare compared to the undomesticated ostrich and zebra. There was no significant advantage in taking a menagerie over the alps, but there was an advantage in the size and shock value of an elephant. Hannibal brought elephants because they were useful in battle, but they were also hard to train, feed, and maintain. Evidence of the difficulty associated with elephants is how many died crossing the alps.