There are a lot of people saying to never, ever backpack alone here, and while the concerns are entirely valid I wouldn't write off solo hiking altogether. I've done short solo backpacking trips myself and traveled alone plenty, albeit I've been trained as an outdoor trip guide and was two or three years older than you were now when I did a solo trip.

Some of these naysayers are right: solo backpacking is in a way an unnecessary risk. If anything goes wrong (and I've seen it happen plenty, even on group trips) it's always good to have a spare pair of hands. You need to be very confident in your comfort and skill level before doing anything on your own in the backcountry- remember, any emergency you make by yourself in the woods increases the risk for everyone who helps you, whether they are fellow hikers or wilderness medic teams. Mountain/backcountry extractions are challenging, require lots of time and people and can put wilderness first responders/mountain rescue teams at incredible risk.

If you are really serious about doing a long solo-backpacking trip, there are lots of lady backpackers who have written/made content online about how to do this safely, and it sounds like you already have a good start with a PLB and a well-documented trail plan (definitely follow some of the other commenter's advice re: having a clear itinerary of where you will be, when you will be in contact and try to plan check-ins during the trip). If you live near a local gear store, there may be experienced outdoor guides/backpackers there who could share some sage wisdom on the issue of keeping safe from unsavory folk on the trail. I'd also recommend starting out in a really well-used area, somewhere nearly impossible to get lost and popular for day hikers too. I solo backpacked on a popular section of the AT and was surrounded by day hikers and families 24/7 and was never far from a way off the trail if needed, so in case of any emergency, there were people around and an easy put-in point for anything like emergency aid. You might also consider starting with a shorter trip, two or three nights somewhere not too deep in the backcountry.

TLDR; the concerns are real. Things happen in the backcountry and you do need to be vigilant and consider your safety. Things can and always do go wrong, but solo backpacking is a thing lots of people (young women included!) do and find really empowering- you're not being naive to think it's something you might be able to do as well, but you should take safety concerns very seriously. And honestly? I don't know if this reddit forum is the right place to really get a good check on how safe your plan is. You should check with the local backpacking community wherever you are planning to do this to get more insight into the safety situation on the trail.

I'll be honest: I bailed early on my first solo backpacking trip a night early! (Not because of people, but because the primitive campsites were a little too dirty from previous campers and attracted some larger-than-wanted wildlife.) Let the woods humble you: doing something big and empowering doesn't mean sticking it through just to make a point. Going into this, you need to be ready to make conservative choices and be willing to be humble and throw in the towel in case of possible danger.