Instructions
Talk to Chancellor Hassan in the palace at Al Kharid. He will send you to his assistant Osman, who will then send you to see his daughter Leela in Draynor Village.
Buy shears from a general store. Use the shears on a sheep to get unspun wool. Travel to the west tower of Lumbridge Castle and use the wool on the spinning wheel there to create eight balls of wool.
Travel to Draynor Village. Talk to Leela when you arrive, and she will tell you about the rescue plan. This is what you will need the wig for.
Travel to Ned's house in Draynor Village and talk to Ned. He will use the wool you have created to craft a wig and rope for you.