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.

If you save all the Little Sister you get the good ending (even if you kill one LS), but if you decide to harvest more than one or all, you will get the alternative endings. There are two, and each one depends if you saved some and harvested some or just decided to harvest all. Though the two negative endings are similar, the 'feeling' from the narrator changes - not the story. You release mayhem upon the real world if you decide to be a killer of Little Sisters.