My, that Daisy dog is just a busy little punkin', isn't she? I don't think that unless you're putting some sort of preservative in the tree's water it would hurt her, but I would try covering it as noted above and teach her to "leave it" and encourage her to play with something or take her to her own bowl and teach her to drink on command if necessary. I wonder if adding Bitter Apple would help? I doubt it would hurt the tree, but it might make the water so yucky Daisy decides she doesn't care for it any more.