I agree that natural light is always best, but lets face it - most houses aren't built to have every room well-lit naturally. What do you do at night time? Buy a lot of lights to place around your house? Or just not take any pictures at night?
style="BACKGROUND-COLOR: #000000"Given your camera which I don't believe has a hot shoe (if it does then the problem can be resolved with an off-board flash). But if it doesn't, then post processing can indeed cure the problem. THe one produce mentioned, Paint Shop Pro does an excellent job. I still use it on red-eye as the Photoshop tool for doing it hasn't produced stellar results for me (could very well be operator error though!!!).
style="BACKGROUND-COLOR: #000000"In any event, there has been good advice here for how to stage some shots but many great animal shots are not staged. If you want a portrait shot, then the lighting suggestion by David French sounds great - but not very praticle for every day use.