My son kicked the binky habit really quickly right before his 2nd birthday. He went through a clingy phase around 18mos, and moved from only taking it at night to wanting it during the day. We decided to wean off the binky before his birthday as he had shown he just liked to chew on it at that point and it was interfering with his talking (he tried to talk with it in his mouth). The process was pretty quick - just talked about how when he turned 2 he was too old for a binky because he would be so grown up, then one day when he asked for it told him he was old enough to go without. He was really proud of this, and actually gave it up willingly. Around 2, it was important that rules were set by some "greater force" instead of made up by us. So, as long as "2 year olds were too big for binkies" my son didn't want his binky.
... It did come back 4 mos later when his sister was born. That time he took it from her as soon as she came home from the hospital out of curiosity - like didn't even know what to do with it! He quickly re-learned what to do with it, and we just ignored this regression, re-enforced that babies need pacifiers to calm them down, and he reasonably quickly kicked the habit again on his own.
Our daughter is 18 mos, and I'm wondering if I will ditch the binky at 2, again. She's not very attached to it, only takes it when she is really tired or needs calming (new situation, not feeling well). It is NOT interfering with her speech because it is not in her mouth much.
I'd suggest playing it by ear. I've heard the habit is easier to kick when the child is younger probably because they don't have the language skills to resist. I've learned tho, that other bad habits (like crawling into bed with me at midnight!) are just as easy to kick later on when the child is receptive to rewards (like extra books at bedtime).
For what it is worth, my niece kicked the habit at 3, and I've heard of others successfully doing it later. I doubt your daughter will need the thing by elementary school ;)