animated film similar to Mulan

I watched this around 2005-08, can’t tell if it’s older than that but def not newer.
I vaguely remember it, but here is what I do remember: It’s set in China and starts with a little girl and her father. She tries to shoot with bow and arrow but is bad at it and some boys laugh at her. She tries again and again and gets better. She has a panda as her companion. Eventually, she grows up and goes away from home on her horse and the panda. I think there was a war going on and there were some graphic fight/death scenes but I could be confusing this with something else. Towards the end of the film she finally gets to her destination and wakes up a dragon which was her goal and the dragon helped her in some way?
The animation was kinda serious and dark, and there was a sound similar to doves flying away that could be heard throughout the film. I could be remembering some (or all) of these things wrong, so give me anything that reminds you of this even a little bit 😀