I took 20 minutes out of my day every day to train my dogs to sit and stay by the door with it open. My dogs are the same way. They will DASH if they get the chance to be outside. However, they now will not exit the door without my permission because I worked on them sitting and staying by the door with it open.
If you are unable to train her to do this for any reason, I might consider putting a baby gate/play yard around the door. It will perhaps limit your fear that she will run out and be in danger.
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