I have a little boy, but I used to cut hair for a living. And I always thought "what's up with the Pebbles Flintstone thing?" Until my friend had a girl. Yeah, there's a reason people go with bangs! Baby hair is too fine and wispy to get it to stay anywhere, especially off to the side.
If you don't mind dealing with clips all day, then go ahead with them, but if it's driving you crazy cut some bangs. Just don't do it yourself!
If you have a hairstylist you love she might do it for you. I really didn't do children's hair generally, but for clients I would often do baby haircuts for nothing if they had their baby with them. It only takes a minute. But your stylist may not be as generous. :) Ask how much she would charge. Don't be offended if she tells you that she doesn't do children's haircuts- it's much more stressful and people want to pay a lot less!
Find a place that does kids hair- don't do it yourself unless you have to. If you have to do it yourself part the section you are cutting *very* carefully, clip everything you aren't cutting off to the side, and check to make sure the bangs aren't going to be too thick or too wide. Take your time. You may end up staying with bangs, you may end up growing them out. But yeah- I vote for bangs! Good Luck!