We do spend a bizarre amount of time dealing with hair in my household. I can't even tell you how many bottles of conditioner we go through in a month :-)
My girls have never had a full hair weave/braiding at WDW. We have, however, had MANY hair wraps at WDW. This is a popular activity at Disney World, and once a little girl sees the wrap station, you're going to need nerves of steel to drag her away from it. Hair wraps are when a small section of the hair is completely overwrapped with a colorful embroidery floss. Decorative beads may be added to the end of the wrap. Prices can change, but currently a wrap costs about $2.00 per inch. Beads are extra and range in price from about a dime for a "spacer" to several dollars for an intricate ceramic bead. A typical price for a child with shoulder-length hair would be about $20-25. However, with long hair, or a taste for expensive beads, the cost could end up being more than that. Get an estimate before you begin.
Hair wrap stands are poolside at many of the resorts including Wilderness Lodge, Beach Club, Grand Floridian, Caribbean Beach and Port Orleans. There may be more as well. The resort stands have limited hours and may change location, so call before heading over. There are also wrap stands on the Boardwalk, at Downtown Disney, and in the Animal Kingdom near the entrance to Camp Mickey Minnie. Other park locations may exist as well. Most hair wraps can be done in 15 to 20 minutes. The wraps tend to last several weeks and can withstand many washings.
Having a full hair braiding at WDW is much less common. You can read a Moms Panel answer about this
HERE. I personally can't recall ever seeing a girl going through a full braiding at WDW like you might see on a Caribbean island. And frankly, with so much to do at WDW, I can't imagine devoting several hours to a full braiding.