Fieberbrunn is an excellent choice for solo female travelers. It's a place well-known for its charm, friendliness and safety. Known mostly as a ski resort town, it is designed to accommodate foreign travelers and hence all facilities are mindful of safety and security. Additionally, Austrian citizens generally have a high level of education and respect for all people, so you are likely to encounter no issues while travelling alone. The crime rate is very low making it safer than most cities. As always though, common travel advice applies: take care of your belongings, be aware of your surroundings, and always tell someone where you're going.