A female ostrich and egg
Ostriches are tameable, rideable mounts found in the desert. There are males (which are black with white wingtips) and females (picture) as well as babies and albinos. The females lay eggs (usually at night) and you can pick them up. However, if you pick one up, the ostriches will attack you. Bring the egg to an enclosed area with lots of torches. Eventually it will hatch, and will grow up. When it's an adult, you can put a saddle or horse saddle on it and ride it. Females are slowest, then males, then albinos, even though albinos are still slower than horses. Don't be confused with the colorful ostrich, which you may find. I'm not sure how it works, but colorful ostriches can be found places other than the desert.