。
I wonder what'll become of her.
Literal
She [topic-は] how become [I wonder-のだろう].
どうなる is the standard frame for 'how will (it) turn out / what will become of (it),' using どう ('how') with なる ('become'). Tacking のだろう onto the end converts the bald question into wistful speculation — the speaker isn't asking anyone, just musing. This pattern of [question word]＋なる＋のだろう is a cornerstone of how Japanese voices anxious wondering about an outcome. Swap なる for the past tense なった and you get the lost-touch version: 'what became of...?'