A baby's first haircut is all about the first. No doubt--it's a sentimental milestone.
But remember, a one year old isn't likely to see it that way.
Kids can be terrified of strangers-- add to that scissors and a strange place. It can be a recipe for disaster. And those of us who try to do it ourselves have learned-- it's a lot harder than it looks. My poor niece barely escaped injury when my brother in law attempted the first cut.
He was using an electric shaver-- it slipped, and she was scalped! It took weeks to grow out. (She looked adorable in spite of her buzz cut!)

So if you fear that might happen to you, check out the areas kid friendly salons. There are quite a few of them sprinkled throughout the area.
Here's a look at one in Avon: