Norway is probably one of the best destinations for women who love hiking and camping by themselves. The land is breath-taking beautiful, you can wild camp almost anywhere, and there is a wonderful net of mountains shelters and well-maintained trails. Scandinavia is generally considered a very safe destination for women, also when hiking and camping solo.
When you hike alone you rely completely on yourself and what is in your pack. That is why you have to make sure you have all you need with you - and not much-unneeded extras, so you don't schlep any unnecessary load around the hard terrain.