I am a man, and so not able to speak to your quesion directly from my own experience. However, I have done extensive solo hiking, camping and bacpacking. I tend to agree that campgrounds and the first mile of trails are the more likely places where trouble could arise from other people, as compared to further uptrail. I also agree that such trouble is not very likely. Keeping you wits about you and trusting your instincts should be enough to stay safe.

When you're on the trail, or you have left the trail to hike cross country, it is the fact that you are solo more than that you are a woman which can cause trouble. Here, too, the key is to keep alert, think things through, and not accept risks without careful consideration. Especially notice when you are bumping into your ignorance, so you see the gaps in your knowlege and take that into account. Never be afraid to change your plan if a challenge looks too big when you finally meet it face to face. Prudence is not weakness, but often wisdom.

In short, if you stay smart, you can certainly do this safely, have a good time and learn a bunch about yourself in the process. Good luck.