Do all kids stutter?

Brody has talked in circles as long as he's been able to string together words. A typical sentence will be "Brody go to pool and Dada go to pool and Brody." As he's nearing two and a half his sentences are becoming more concise but we're starting to notice a new trend- a stutter. He often repeats the first word when he's excited and struggling to get the rest of the sentence out, but that's not what I mean by a stutter. Over the last week he's developed a true stutter where just the first sound is repeated. I wonder if this is common and if all kids stutter a bit while they're learning to talk. I'm interested to see how this changes as he becomes more comfortable with his words and his ability to communicate. For now, we'll just keep watching and listening.