Caroline and Olivia are two of my favorite names! Olivia is popular, but you could call her Libby or Liv to make it a little different. All of the Olivia/Alivias I know go by their full name.
I agree with the nickname thing about Caroline. I despise the name Carol, and the only other NN I've heard for it is Lainey, which I also am not a big fan of. I don't know... if you only ever call her Caroline, it's probably what she'll get used to and go by. Unless she's a rebel in her teens/twenties and feels the need for an identity change. I feel like that happens a lot. I know a girl named Rachel that started college using her MN only, Elisha, and a few girls I've known have changed from Katie to Kate or Katy, or from Liz to Beth. So I guess you have to decide if you're okay with that possibility.