If you are going to buy a new camera for your African safari, then I suggest you buy a digital SLR camera.
Both Nikon and Canon produce very good, affordable digital SLRs. You will need a good size telephoto zoom lens, at the very least a 200mm lens, and ideally a 300mm lens. Nikon and Canon also have lenses with new technology called Vibration Reduction on Nikon and Image Stabilization with Canon. These lenses have a feature which you can turn on to reduce the old problem of camera shake.