One meaning of the word hunt is just to search for something. I don't see any problem in vegans using it and little point trying to "protect" our children from a word. It's good your daughter uses words appropriately, she will learn soon enough that many words have multiple meanings.
As far as the easter egg hunt? I avoid them for their pseudo-christian-pagan mumbo jumbo content, not beacause they aren't vegan. Although, I would prefer bird eggs not be seen as something to use for a frivelous game.
I try to avoid dragging too many things under the vegan umbrella. Vegan means not exploiting animals period, neither of the above activities exploits animals, therefore are fine for vegans.
I don't think trying to shelter children from every non-vegan thing will be very effective anyway.