To reiterate what ZombieWife said, it is fantasy, therefore it's up to you. If everyone must do things a certain way then we need to find a new word for the genre. Stories filled with inequality, written under the excuse of 'it was a different time back then' do little for me. Sometimes I can be quite suspicious of a writer's motives for emphasising inequality, especially when it adds nothing to a story. (Different when the story is
about inequality, and an MC's struggle against it.)
IMO, it's not about strong/weak, it's about gender stereotyping. And it's everywhere - every nook and cranny of the world: real, portrayed and imagined. Art is the perfect vehicle to slowly change perceptions and shake things up.
Why don't you try changing the gender of your character once you've written a first draft? If something jars, then you've probably got some gender stereotypes in there (obvs some actions are inextricably tied to gender, like giving birth etc. Miiind you, you're writing fantasy, aren't you?
)
Katniss Everdeen is a brilliant character, because she could be either man or woman. Similarly, in 'Frozen', Elsa and Ana could also be brothers, and the story or dynamics wouldn't change.
Good luck
Let us know how she develops!