When you speak, sing, or utter any kind of sound, you vocalize. A tiny baby can only vocalize gurgles and coos, but by the time she's three or four, she'll vocalize all kinds of opinions.
Vocalize literally means to make a noise using your voice — in fact, vocalize is rooted in the Latin root word for "voice," vox. It's nearly a synonym for verbalize, "put into words," except that when you vocalize you may speak using words or you may merely make noises. So while your dog is smart enough to vocalize a response when you say, "Speak," he's still not smart enough to verbalize.