It's really difficult to choose a manga with a heroine in that age bracket without any romance whatsoever. They exist, but mostly in the slice-of-life genre, rather than fantasy. So, the below fantasy recommendations will most likely have some aspect of romance, though they aren't the main focus.
Akagami no Shirayukihime An adventure, fantasy romance. Shirayuki is a fairly strong and independent character in her own right, and she does a whole bunch of great things on her own. There
is quite a bit of romance, though, but it's the really, really sweet and innocent variety. (You could try one of
Akizuki Sorata's oneshots beforehand to get a taste. She's usually pretty good at writing nice females.)
Akatsuki no Yona Yona starts out a bit weak-willed but she really grows as a character as the story progresses. It's a fantasy, adventure. She also has a harem of guys but they all treat her with the respect she deserves, I think. There's also probably going to be romance later on, but six volumes in and it hasn't surfaced yet, so...
Aqua /
Aria Most of the main characters are girls in this one, and it's a really wonderful and beautiful slice-of-life about appreciating the little things that life throws at you. It's fantastic, and I really would recommend it to everyone. It's not really fantasy, though there are some parts that are pretty fantastic. No romance either.
Gisèle Alain A really lovely story about a young girl trying to help others and find her place in life. No romance, really, but also no fantasy either. (It's a historical slice-of-life.) It's also a seinen, and while it's usually pretty kid-friendly, there are a few scenes which might not be, though I doubt your daughter will notice. I remember skimming over all the "adult" stuff I didn't understand back then and had no idea what they meant until much later.
Kieli A fantasy adventure that actually does not have any romance! It's a pretty nice read, with good characters and a good backstory and plot. It's not incredibly good in the way that I would recommend it to everyone, but it is nice for a little diversion, and especially nice if you want a good heroine in a quick adventure series. (The light novels are licensed too, actually, so you can also pick those up if your daughter likes the world in this one or something.)
Otoyomegatari A great manga with strong women and an incredible art style that blows me away every time I read it. There is romance here, though, and it's not really a fantasy, but it's so fantastic that I just
have to include it.
Saiunkoku Monogatari Oh man, Saiunkoku Monogatari is
great with its portrayal of women, Shuurei in particular. It basically details how the main character Shuurei manages to gain power and authority in a time completely dominated by men. And while there
is some romance, it definitely isn't the focus. Shuurei's drive to succeed is definitely the driving force of the plot, and her struggles are infinitely relatable and inspiring.
And, from my experience,
Hikawa Kyouko is extremely good at writing nice female characters in a fantasy setting, though all of her works have romance as a plot point as well. Her
Kanata Kara is excellent though and really shows that a female doesn't have to be
physically strong to be a fantastic character.
Oh, and if you don't mind the girl not being the main character, I would recommend pretty much anything by
Shirodaira Kyou. (The females are usually the second main character or a major side character.) He's usually really good about writing decent female characters, in
Spiral and
Zetsuen no Tempest especially (though the latter has romance).
Also, does this mean you're looking only for licensed manga? If so, then only
Kieli,
Otoyomegatari,
Saiunkoku Monogatari,
Kanata Kara, and the works of
Shirodaira Kyou would be applicable. (
Aqua /
Aria have been licensed, but their licensing company went defunct, so.)
