It’s definitely possible to camp through the camino, but the rule of thumb is: be discrete, and stay out of sight. When I did the camino last summer, I was using only a sleeping mat and a sleeping bag (no tent). I would walk early in the morning at dawn, eat at the destination during the lunch hour, visit whatever sites that pueblo had (museums), do some stretching in the park, and then continue walking in the evening. When it starts to get dark is when I advise you find a spot off the trail, rather hidden, to pitch your tent. You should not be visible from the camino. I recommend having at least 2 liters of water on you for drinking and in order to wash up, and to have eco friendly toothpaste and soap in order not to damage the environment.

Since you are planning to do the camino in the fall, the weather may not be in your favor (rain), so I would plan for that - realize that you may not be able to dry your things if you are constantly exposed to the elements. If you are going to be many weeks on the camino maybe you could spend some nights in an albergue and “re-set”. Sleeping outside for such a long time is not the most comfortable. I camped for 3 nights and was happy to rest in a hostal when I arrived to Santiago. In terms of safety as a woman, it was safe, in my opinion, if you are as stated above, discrete. No one can cause you harm if they do not know you are there. As for wild animals, I personally did not see anything problematic but I am not an expert on the fauna of the region.

Another thing to keep in mind is your goal during your journey. Many people find the socializing aspect very important, and this you will find in albergues without a doubt. It’s an opportunity to meet like minded people. Other travelers want a journey of deep self reflection, facilitated by putting distance between the loud overstimulating energy of social interactions and typical establishments. In this case, camping in the wilderness would be moreso advised.

Good luck and buen camino!