It's cute, but very overdone here. I known probably 14 little Avas.
Aviva and
Avia are cute suggestions, I like
Avis, and I don't think
Eva or
Eve will ever become common, let alone super common.
As for suggestions, I adore
Ada and
Adah (I prefer the H at the end, but I'm in the minority on that I'm sure.) It's so beautiful and regal.