It's probably one of the many newly created "American", often "African-American" names that makes use of Native American words and combines them with words from other, often none-European words/names.
In this case, there is a Native American (specific language not designated) word, Sha- which according to one of my name books means "pelican". Therefore, I would suspect that it would have been most common among the Native Americans in the southern states, specifically Florida and the Gulf Coast.
Many African-Americans have combined these words with a variety of endings most likely to reflect their multicultural background. The endings tend to come from a variety of sources including Swahili, Arabic, Yiddish, Hindi among others. There is a Swahili word Dinka, that means "people". The sounding of the last syllable of your daughter’s name is similar and that is often enough to be the actual root …the language of names is often difficult to discern.