Lots of animals maintain balance without whiskers, which makes sense because whiskers have nothing to do with balance. All vertebrates share similar balance organs, which developed at the center of the skull long before the evolution of hearing. In mammals, the inner ear—which connects to the middle and external ears—tracks movement and regulates balance.

Whiskers, on the other hand, began evolving 120 million years ago along with early mammals. They're called vibrissae, technically speaking, and most mammals have them. Broadly speaking, vibrissae act as feelers: they are organs of touch.