From what I saw in previous articles, Fuddy was visiting the sparsely populated island of Molokai to inspect the leprosy colony there, which. pursuant to Hawaii state law, was under her jurisdiction as the head honcho of the state's Department of Health. Her visit was reported as routine.
As to why she was on that particular plane, the intuitive guess is that she didn't really have any other choice but that one airline which flew passengers in that particular Cessna model aircraft between the two Hawaiian islands of Oahu (on which Honolulu, Fuddy's main base, is located) and Molokai. It's a very short flight, about 50 miles.
http://hawaii-aloha.com/blog/2013/06/11/makani-kai-air-expands-flights/
“This is great news for the isolated island of Moloka‘i, which has an airport too small for large planes. Makani Kai specializes in smaller turbine and twin-engine planes (nine passengers per flight). The carrier also operates Makani Kai Helicopters...”
we have leper colonies in the USA???