I ran across
this article about coconut oil for dogs, which was pretty interesting. Excerpt:
Dogs and humans can both benefit from unrefined or virgin coconut oil, and dogs love the taste. It is important to start slowly, building up to the recommended dose. Coconut oil can cause detoxing symptoms as it kills harmful bacteria, viruses, parasites, yeasts, and fungi- so headaches, fatigue, diarrhea, and flu-like symptoms are common if given too much too fast.
So you might be on the lookout for that, but otherwise it sounds like you'll be fine.