Having walked the
Camino Frances once by myself and as the mother of a daughter who turns 18 today (!) I would be happy--thrilled even--to let my daughter walk by herself. However, I would discuss/plan for some things before she went (albeit my daughter is a fairly experienced traveler and I don't know if you are). I don't mean to say that you will need to do these things, just that they are what would make me, the mom, feel comfortable. Here they are:
1) I would send her with about $200 Euros cash. I usually just get Euros at an airport ATM in the first place we land, but a young woman traveling alone should have more of a safety cushion, I think. Of course, I'd send her with a debit card with 4 digit PIN, AND a credit card as well.
2) I would have her bring a smart phone with International calling enabled and both Viber and WhatsApp loaded. I would ask her to contact me everyday and encourage her to just call on days when she couldn't get sufficient WiFi to do so for free. The occasional ~$1 for a short one minute call would be worth it. I wouldn't be comfortable waiting for her figure out how to get a new SIM card or purchase a new phone upon her arrival.
3) I would be sure she knew what having one glass of wine (maybe even two) with dinner felt like so she could decide for herself if she could be aware and alert enough after that or if she would prefer not to drink. US kids sometimes only have experience drinking to get drunk, which of course you wouldn't do on Camino, right?
4) I would counsel her to reserve some energy for the unknown. The biggest difference I noticed between the young and the old(er) pilgrims during my walk was that the young were much more likely to push themselves to their absolute limits, and sometimes that caused them to end up in difficult situations. Twice I helped young women to albergues when they were too sick or exhausted or both to get there themselves. Take time off if you are sick, and don't walk to the point of utter exhaustion, even if it means you have to use transport other than your own feet to make it to your flight home. You can often call a taxi even, if needed!
5) I'd ask her to pay attention to her own radar for danger. If a situation makes you uncomfortable, find a way out of it right away and don't second guess yourself. It only happened to me once on the Camino (entering the city park on the way out of Burgos in the dark), but I'm very glad I waited outside the gates for a British pilgrim couple to walk with. Maybe nothing would have happened, but my radar went off and I listened so nothing did happen.
6) Most of all though, whether she went at 18 or 58, I'd want my daughter to have fun and be open to all that the Camino would bring her, and that is my wish for you too!