The phrase 'make her way' is correct and usable in written English.
You could use it in a sentence such as: She grabbed her purse and made her way to the door.
She would die trying to make her way toward Jerry.
Bartlett was unable to make her way back to Vashisht.
Somehow she managed to make her way into the stairwell.
I stood with him, waiting for my mother to make her way outside.
And I take pride and joy in seeing Emma make her way so confidently and capably.
Intimidated, and shy of contact outside the family, she found it hard to make her way.
Mamounia intended to stay with Father Bernard until her wounds healed and then make her way to Cameroon.
Alone, she then had to make her way back through the crowd of men before walking the three miles home.
As he watched Charlotte make her way up the street, Stevick experienced only relief that she'd refused his suggestion.
She was 69, simply trying to make her way home, when a heedless driver took her life.
Safural tried to make her way to the exit, but found her route blocked.
