NO, it is not finished.
The anime finished before the manga:
Anime finished: September 16, 2011
Manga finished: December 08, 2011
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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Usagi Drop centers on Daikichi, a bachelor whose life takes an unexpected turn when he learns about Rin, his grandfather's illegitimate daughter.
Finding Rin isolated and unwanted by the rest of the family after his grandfather's passing, Daikichi impulsively decides to take her in.
The anime follows Daikichi as he navigates the challenges of becoming a single parent, despite having no prior experience with children.
It's a heartwarming story about building a unique family bond and discovering the joys of caring for another person.
The series explores the development of Daikichi and Rin's relationship and how they both grow and change as they learn to rely on each other.