It may not be the binky. Some kids just talk late. My son is 16 months old and he only says "go". However, he communicates clearly in other ways like gibberish and pointing. The whining and tantrums may just be because she wants to express herself more clearly but doesn't know how. Taking the binky away may help, but it may not. The important think for this age group is that they are communicating. Can she follow simple instructions (ex: Pick up the block. Put this in the trash.)? Does she respond to her name? Does she respond to your voice? If she does these things then she is probably right on track.
However, if you decide to get rid of the binky, I have seen a lot of success with my friends who have kids by having the "binky fairy" visit. Essentially tell your daughter that the binky fairy needs her binkies to give to babies who don't have any. Then collect all the binkies, put them in a bag and put them on the front step. Before your child wakes up in the morning replace the binkies with a prize. My friends' kids were so thrilled about helping other babies and then getting a prize they never asked for their pacis again.
Okay. So now that I have typed that up i realize your daughter is 15 months old and may not have the critical thinking skills necessary for the binky fairy. With kids that young you could really just try going cold turkey or weaning off the binky. Maybe you could let her have it at bedtime, but no other time.