While the exact age at which to intervene on those children who practice non-nutritive sucking (such as pacifiers, thumbs, etc) is somewhat debated, it is generally considered to start intervening at about the age of 3, as you suggest.
Before that time, it is difficult to understand and to teach young children. The consequences of continuing to suck thumbs or pacifiers include increased rates of ear infection, other types of infection, and possibly even the potential for deformity of the facial bones due to the constant forces that are applied.
Fortunately for you, children who suck a pacifier are generally much easier to wean from this than are those who suck their thumbs. There are many strategies that your doctor or dentist
will be able to recommend, including everything from positive reinforcement to dental devices that make it difficult for the child to suck his or her thumb.
Additionally, your health care professional will be able to speak at an appropriate and authoritative level to your child so that they are even more likely to respond appropriately. Please speak to your pediatric dentist
about helping your child to stop sucking on her pacifier.