In Mexico there is a state (and a city) called Puebla. The name given to people (or things) from that state is "poblano or poblana". La Poblanita is a diminutive of "poblana". So, La Poblanita is like saying the little woman (or girl) from Puebla. Cheers.
P.S. Be mindful that Puebla is a relatively common name, and there are many towns in the Spanish-speaking countries (I think mostly in Spain) with that name.