Midshipman's Hope is the first book in the Seafort Saga by David Feintuch. I don't care for coming-of-age stories or books with adolescent protagonists, but that's exactly what this is and I like it fine.
from the back of the book:
A hideous accident kills the senior officers of the UNS Hibernia -leaving a terrified young officer to save three hundred colonists and crew aboard a damaged ship, on a seventeen-month gauntlet to reach the colony of Hope Nation. With no chance of rescue or reinforcement, Nicholas Seafort must overcome despair, exhaustion, guilt; he must conquer malfunctions, mutiny, and an alien horror beyond human understanding.
He must save lives. And he must take them, in the name of duty...