Symbolism, Imagery, Allegory
The peacock is the most prominent, as he should be. But a quick look around Strega Nona's home also reveals that she has at least one bunny (10), a goat (11), and some bird friends (5, 13). And of course there are doves throughout the book (2, 3, 7, 9, 26, 27, 29).
All of these animals help to link Strega Nona to the natural world, which is another endorsement of her magical abilities and a testament to the fact that she fits in with nature, instead of going against it. And the doves in particular, which can be directly linked to the Bible (it was a dove that brought the olive branch back to Noah's Ark to indicate the flood was receding), once again demonstrate that despite her use of witchcraft, Strega Nona is not a threat.