K.N.
Are you sure this is not being prompted from teething or gum sensitivity? If you give her some infant tylonal, do you notice a change in her oral fixation? If so, she might be soothing herself with teething issues.
Around 15-18 months my DD had a rocky time with teething, because her canine teeth (aka: cuspids, eye-teeth) and her molars were coming in. Does your daughter use a pacifier? I know, everyone wants to rip the binkie out of their baby's mouth around age 2... But I noticed that without a pacifier, my DD would gnaw on her hands and fingers much more... and that made me worry about thumb sucking or nail biting habits developing, Yikes, those are much harder habits to break!
Maybe you can see if one of those mesh food sucker/biting gadets will help... (ya know, these things: http://store.babycenter.com/product/code/3925.do. I think Target has some-?) Stick some frozen banana or fruit chunks in and maybe that will help divert her habit of finger gnawing and nail biting...?