Lighting conditions will be important, of course, and the better the light in the environment the more likely it is that you'll come home with a few nice snapshots. If the zoo has buildings where one has to go inside to see and photograph the animals, that is more problematic in terms of light, especially at that fully-zoomed-in point of 40X/960mm, and if one is handholding and not using a tripod or monopod chances are much higher that there will be motion blur and such.
When shooting animals and birds, always aim for the eyes, yes, and also try not to inadvertently clip out an important body part of the animal or bird -- that is, don't clip the fully-extended wings of a bird in flight, or show only part of a Lemur's tail when you've managed to get the rest of the body just finel, and don't whack off the ears of a mammal when doing a head shot.... Sharp focus is important, too, showing fine details in a bird's feathers, a mammal's fur, whatever....
Have fun, enjoy the zoo and its inhabitants, and shooting photos!