It is grammatically correct and pretty good as it stands. You might replace One day, her mother was going to give birth, so the little girl with Her mother was going to give birth soon, so one day the little girl. This allows more time for the action to unfold. The way you have written it, a suspicion may arise that the birth is so imminent that the little girl will not have time to cross mountains and valleys to fetch the midwife, shoes or no shoes.
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