It is partly on account of Hera's great beauty, and particularly her beautiful, large eyes, that she is linked to her sacred animal, the peacock with its iridescent feathers having "eyes". The peacock symbolizes her luxury, beauty, and immortality.
This animal is very sacred to her, you are not getting her personal peacock but one chosen specifically for you by her. It is a great honor and one I don't think she bestow's lightly and I am humbled by her generosity.