My DS turned 2 two weeks ago. I warned him the week before his birthday that on his birthday we were going to a special fair (a county show) and that at the fair, we were going to throw his dummy in the bin and in return he'd get chocolate buttons (smarties).
I said it so often that we got to the point where if I said dummy, he said 'bin'.
So at the show, we duly went over to a big bin and I asked him if he wanted to say bye to his dummy and get chocolate buttons. He gave it a last suck and then threw them in the bin (I have to say, I nearly cried - it was an end of an era).
Anyway, he got his chocolate buttons. When he got tired later on he yelled for it but we didn't have it so couldn't give in. He fell asleep.
He was unsettled the first two nights - but not nearly the screamfest I expected. He spent one week waking at night and now he has completely forgotten about it. Well nearly - he still occasionally asks for it if upset - but I just say: where is your dum? And he says: bin. And we move on.
Honestly, a lot easier than I thought it was going to be. So I would say, whatever you game plan is, give warning, have a treat in store, don't back down and don't have any in the house. Ride it out. It will be over soon. Good luck
PS - you should also try to cut down on dummy use before you get rid of it - so only let her have it at naptimes for example. That way it's easier. Also introduce some of other kinds of comforter - like her blankie or a teddy as a replacement.