We've done it for all 4 of our boys, and I love it! In fact, we get the boys haircuts here almost every trip - for a while our kids thought you had to go to Disney for a haircut! If you have an appointment it doesn't take long at all, they get to you pretty fast after you check in if you are a few minutes before your appointment time. Your child can sit on the riser they have that fits over the chair, and you can sit right in front of the if they are small and could fall. They also can have you hold them if they cooperate better that way. It doesn't take long for a haircut if it is a first cut for a young child, and they are used to working with kids who can be fussy.
The only difference between a first haircut and a child's haircut is you get a first haircut certificate and a Mickey Hat that has first haircut embroidered on it, and the price is $25 instead of $19 (not completely sure about the prices). I think it's well worth it, but that can be subjective I'm sure. They also make a point of setting up a picture where the kid has the hat on and is looking in a mirror, and taken from behind you see the first haircut on the hat, and the child's face in the mirror. It's cute, but can be hard to get perfect.
A tip I didn't learn until our most recent first haircut experience is that when you check in you can ask if there is a photopass person available, and if there is a roaming one they will come over and do PP pictures of your child's first haircut. They were able to do that for us last time, so we got photos of our twins' first haircuts and our older boys haircuts as well. She took a ton of photos, and was super nice.
Another tip is to be careful around parade times, it can be very difficult to get there if any parade - including the Move it Shake It one - is going on. If you get stuck and are late they then treat you as a walk in and you have to wait- ask me how I know

. There is a door from the Emporium right near it that you can often pop out of and get there, though.