I have some names I like, but I don't like an obvious nickname, for instance I like
Frederick but dislike
Fred.
Otherwise, I find it's mainly people in English-speaking countires who seem to feel this need for nns. Unless maybe a bane's super-long, there's no necessity for a nn. So I think that, at least until your daughter's young, you could just call her
Alice and discourage others from using a nn. Of course, once she's old enough to decide for herself, then she might want to go by
Allie or Liss or some other nn.