While it's not strong in the romance department,
Kemono no Sou-ja Erin is an excellent show about a young girl who can communicate with mystical beasts.
Noein is a science-fiction story, but like many Japanese sci-fi shows, it's not that far removed from fantasy. More romance in this show, and some remarkably animated action sequences.
Saiunkoku Monogatari is an excellent fit, but it's rather hard to find these days because it's in licensing limbo.
I'll also suggest
Claymore. It strong on the action component, less so on the romance. It's pretty violent in places; the first episode gives you a pretty good idea what's involved.
My daughter enjoyed watching all these shows when she was about your age.