I've always like Millie. It's old-fashioned and quaint. Of the options you listed, I like Mila. Emmy is cute, but I'm so tired of hearing Emmy/Ellie everywhere.
The mother of the only E-milia (as opposed to Amelia) I know calls her "E". Not one of your options, so I don't know what to tell you other than I think the right nickname will just come naturally when you apply it to her.
Let the nn come naturally.. I'm personally not into forced (or planned) nn's. My friend's daughter is named Emma, but they have taken to calling her Emmaroni.. Which is super cute and unique to her. And I think more meaningful. My kids' nn's don't even have anything to do with their real names. So give her a nn as you get to know her
I agree with PP--nicknames should come naturally. My daughter is Amelia and her NN isn't a variation of her name at all--it came from came from something that happened with her. NN are (IMO) supposed to be personal and unique--I grew up with a kid NN'd Scooter cuz when he was 3 he got into a box of Scooter Pies; he's in his 40s now and he' still Scooter :-) My nephew's NN is Juju cuz he that's how he pronounced his name (Jared).
Re: Nickname for baby Emilia
TTC #1: February 1, 2014
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"Everybody wants to be happy. Nobody wants to feel pain but you can't have a rainbow without the rain."
Not one of your options, so I don't know what to tell you other than I think the right nickname will just come naturally when you apply it to her.