I have never known anyone named
Caroline. So I was tempted to do what people sometimes do under those circumstances and say, "No, it's not too common because I've never known one." But I resist the temptation. All one can do to answer the question is to look at the popularity statistics. It's number 62 in the US and has generally been rising. So based upon that I'd say not too popular at the moment, but could become so.
I really like
Caroline and I'm with you in that I prefer it without a nickname.
Especially not
Carrie, which is so 70s dated and annoying anyway.