Nobleandmostancient are you justified too?
Going against just about everyone on this page, I think you should do it.
Do it, use it as a first name. For heavens sake it's not like you're calling a boy Shirley in this day and age.
How many girls are called Andy anyway as a nickname?
As for her constantly being mistaken for a boy, sure that can happen until they meet her but surely that happens now for anyone called Chris or Jamie/Jaime, Frances/Francis and a whole bunch of other names in common usage.
I have one of those sorts of names that like the above has a specific male and female spelling, yet people often use the incorrect spelling or assume I'm a bloke until they meet me. I've never been in a situation yet where it's been or any consequence other than someone saying "Oh, I was expecting a boy, silly me!". Actually, it can often prove an excellent ice breaker at job/uni/etc interviews or other social situations!
My daughter also has the joy of having the middle name of Elliot and frankly DP and I love it! I know this sounds a bit weird, but you know what sort of person your DD is going to be best and it's your decision.
Personally, I like your choice!
If it helps, when I was looking for names, I thought something that people can spell that isn't to widely used, that you like, is a winner.