There are two major reasons to write the novel from Karana's point of view. First, she is the major character, and is alone for much of the text; telling the story from an omniscient POV (point of view) or from the POV of another character would lose the personal and intimate feelings created by listening to Karana tell her own story. This is reflected in the text, as Karana copes with losing first her tribe and then her brother:
The thought of being alone on the island while so many suns rose from the sea and went slowly back into the sea filled my heart with loneliness. I had not felt so lonely before because I was sure that the ship woud return...
(O'Dell, Island of the Blue Dolphins, Google Books)
The second major reason is to better understand Karana's internal thoughts when interacting with modern civilization. The modern reader can more-easily understand the modern perspective, but may have trouble understanding a more primitive perspective if it is simply explained by an unseen narrator. By allowing Karana'a personal voice to become familiar, the reader is given a deeper and more intimate understanding of how she feels when interacting and observing modern civilization.