Will killing a Little Sister change the game's ending?

You should be OK, as long as you avoid harvesting any more little sisters.

From the IGN Game Guide (my emphasis added):

There are two possible endings for BioShock that depend on how you treated little sisters throughout the game. If you choose to "harvest" more than one little sister, you will get the bad BioShock ending. If, however, you "harvest" no more than one little sister but "rescue" the others, you will get the good BioShock ending.

However, there are two bad endings, depending upon how bad you have been. Various YouTube videos show them all.