My youngest granddaughter had her first haircut at a shop where she had a little car instead of a chair, and she was fascinated both with the car and with what that lady was doing in the mirror.
In contrast, a friend took her son for his first cut, and he had a meltdown.
So take your choice.
Before my oldest child had his first haircut, I talked to him about how haircuts don't hurt. We walked by the barber shop a couple of times so he could look in the window and watch. When the big day came, his daddy went with him, and got his hair cut first, so that his son could witness it.
I wouldn't try it myself if it's the first time. Barbers know how to watch for moving heads and stray ears. They may definitely be able to do a better job.
If your barber is an experienced one, he (or she) may have a preferred way of dealing with a toddler.