First, you should stop thinking in terms of zoom. Think in terms of focal length. Zoom means nothing without knowing the focal lengths. You would be much better off optically if you went with a lens that does not go wide. A walkabout lens and nature photography sort of conflict each other. For nature shooting, look for something that starts in the 70-100mm range and goes to the 200-300mm range (70mm to 200mm is not even a 3x zoom). If it falls in your budget, look for something that has a wider aperture as well (i.e. f/4 or smaller through the entire range). Zoos can be somewhat low light due to shading for the animals. Something that is widest at around f/5.6 just might not be wide enough to get your shutter speed up. Also, since you plan on shooting subjects that do not move much, having IS might help. If you are shooting something like sports, then your shutter speed is already going to be fast enough that IS is taken out of the picture. Also consider using a tripod or monopod.
Kevin