I think this camera has built in red-eye reduction. I've never gotten red eyes but I've gotten yellow and green eyes.

For pictures where I actually care whether there's yellow/green/red eye (photoshoots), I usually have a lamp beside them or blast all the lights in the room. Then I set it to action mode where it's less likely to blur and take it from there. The lighting makes all the difference in the world. I just did a little photoshoot with a lamp beside them and they nearly looked professional.