Sorry for the length of my response, but I included details of our process in case you decided to try it.
Just remember you have to be ready to go through the process more so than her because you have to be ready to respond to her needs with patience but without the binky. No one but you needs to be the one to decide this. I've had family members telling me that my daughter needed to get rid of the binky since before she turned one. The binky went away when my husband and I were ready. We chose to do it over a weekend in case we had a sleepless night or two.
My daughter will also be two and a half in December. She had a visit from the Binky Fairy about six weeks ago. Since then, she has asked for the binky one time after which I reminded her the Binky Fairy had it and she went to sleep after a round of other excuses. She has a routine of excuses to get mommy or daddy back into her room but this was going on before the binkies went away. Here's what we did...
I got prepared first. I started talking to my daughter about how big girls don't have binkies. I bought a small, stuffed Mickey Mouse, a character that she loves! I wanted the Binky Fairy to leave something that she could sleep with since she wouldn't have the binky to go to sleep. I put it in a decorated gift bag with a note from the Binky Fairy, thanking my daughter for the binkies, telling her what a big girl she was and that Mickey was for her to sleep with now.
On the day of the visit, we sat down and talked about the Binky Fairy coming to visit and that the Binky Fairy needed more binkies to give to babies that didn't have any. We talked about what a big girl she was now. We got a big box and decorated it up with ribbon. Then she took a crayon and "wrote" the binky fairy a note asking her to give the binkies to a baby that didn't have any. She put the binkies and the note in the box. Then we put the box in her bedroom so the Binky Fairy could find it.
We got ready to leave on an outing. While my husband put our daughter in the car seat, I went back in for "something I forgot". I put the gift bag and note in place of the the binky box, threw the binkies in the trash where she couldn't see them and put away the box they were in. There was no going back now.
Our outing involved a lot of activity so my daughter was very tired on the way home and had fallen asleep. This was done so she would go to sleep easier. Unfortunately, she woke up when we put her to bed. She was crying for the binky and wouldn't go back to sleep. We let her get up and after mommy read the note from the Binky Fairy, she unwrapped the present. She went back to sleep with Mickey in arms.
As I stated earlier, she has asked for the binky only once. I've discovered that she has to stay on a good schedule for naptime and bedtime in order for there not to be too much drama now that the binky is gone. If I put her down for a nap after her normal time, there is a lot of crying and fussing. She doesn't ask for the binky but she wants other things.
Now when she goes to sleep, we give her choices of who she wants sleep with, Mickey or her teddy bear, Mickey or Elmo, Elmo or her stuffed puppy, etc. This gives her control with limits that are acceptable to us but the decision is ultimately hers. Our Binky Fairy was successful. I wish you well with whatever you decide to do. Good luck!