1- suggest she do some local touring first. Multiple weekend overnights and a 4 day tour too. That will help her figure out what to pack, how to pack, and quietly help show you that she has the skills/ability/mindset to fulfill her dream.
2- bear spray for sure. This isnt just because she is a woman- its simply smart to have while crossing a decent bit of the US.
3- no need to bring a firearm, i get that you werent serious, but even suggesting it almost derailed the thread. It isnt needed for all the reasons already listed.
4- ignore mtbaddict. He has 0 experience and is posting off of ignorance and fear.
5- if your daughter is like many(most?) 25 year old women who are active, she is hardly new to situational awareness. Its an unfortunate reality of our society, but one that is overcome millions of times a day too. She probably has more situational awareness than you, even though it may be tough to conceptualize. With 2 daughters and 3 close nieces all between 11 and 15, this is an issue that I think about a lot, for obvious reasons. It sucks that it has to be considered at all, but someone who is 25 and wants to go tour has considered the downsides and is confident they still want to go- so support it.
Maybe meet up and ride part of it too? Not as a way to oversee the trip, but to enjoy part of it with her.