Vietnam overall is a very safe country to travel in and easy to get around. The transport network is extensive and there are many backpackers going along many routes throughout the country. The north has the least foreign visitors but this area is one of the most beautiful in the country!
For solo female travellers, Vietnam is a very open-minded, fair and welcoming country and is relatively free of serious hassles for Western women. The biggest problems for travellers are motorbike accidents and some money scams in the big cities.
There are still undetonated landmines in Vietnam leftover from the War, so be careful about going off into the wilderness from well-travelled rural roads.
With any country, keep your valuables close to you and ensure you have locks on your luggage. A money belt is advised.