The end of March is the start of the early 'high season' on the VDLP, so C Clearly is right - there will definitely be people around. I walked last year at that time and had as much company - or as little - as I wanted. When you are walking on your own, other pilgrims do tend to watch out for you -- if you make yourself seem open to them (and if it seems like that kind of regard would be something you would like). Sticking to the fairly standard stages will increase the number of people in the albergues at night. Eventually you may find yourself looking for a bit more time on your own!
Walking a camino is a good exercise in getting more confidence about doing things that women are often told are too risky.
I am a teacher and I often despair at the things that my female students (who are usually around 20 years old) think they cannot do because it would be 'too dangerous' -- things like go for a walk or a run in a nature park.
I remind them that most violence against women happens in women's own homes and, in Canada and the U.S., the statistics show that more than 80% of violence against women is commited by people they know. I always try to take those statistics as a reminder not to make my life smaller than it needs to be. A camino is a great way to make life bigger.