M.W.
In my opinion, he most certainly IS old enough to discipline. I started disciplining my children at aprox. 9 months. If he can understand the word "no" then he can be disciplined. You will regret it if you wait much longer to introduce discipline.
Please don't misunderstand... Discipline does not necessarily equal punishment. However, if he doesn't have any consequences for the behavior, he has absolutely NO reason to stop.
My daughter developed the same behavior when she was 9 or 10 months old. What worked for me was LIGHTLY tapping her on the lips. Not too hard, but hard enough to get her attention, followed by a very firm "NO screaming!" If she continued, she went into time out, which was served in her crib. I would stand just outside her door, where she couldn't see me, for no more than a couple of minutes... just long enough for her to be briefly upset that she was confined and alone. Then I'd get her, move down to her level, look her in the eyes & tell her again, "NO screaming!" It took time and consistency. I had to literally go through this process over and over, all day, but it did eventually work. (I honestly don't remember how long it took. My "baby" is now 18 years old...)
You are correct, it is a phase, but the longer you wait to address ANY unacceptable behaviors, the harder it's going be to stop them.
Good luck!