Not sure if you have a trip planned or want to wait for her haircut until you go, but Disney's Magic Kingdom has a small barber shop right near the Mickey Fire Station when you walk into Magic Kingdom that does an AWESOME 1st haircut and its CHEAP! We heard about it last year and took our daughter for her 1st cut and she LOVED it. They are very good with kids, the kids are given stickers all over and Disney toys to play with while they are up in the raised chair. Plus,they are already so excited about being at Disney that they are distracted from thinking anything negative about the experience! After the cut/trim whatever you want, they will put it up in a pony or clips,whatever you choose and it stays out of their face all day! They can add a little gel and pixie dust too (girls love this!). They save the hair clippings in a napkin with a Mickey sticker, give you a 1st haircut certificate AND a set of Mickey ears with 'My 1st Haircut' embroidered on the back! This is all for like $10 or $14 (I can't remember exactly). It has been SOOOO worth it. We did my sons this year at 15 mo and he cried at 1st but they were great and he stopped and got a cute cut. They expect everyone in there with cameras/video too.
Go during a parade, lines are shortest. There are no reservations. Good luck! We will do it whenever we go now!