Hi summer
I think touring alone is very reasonable for a woman. That isn't a blanket statement, rather it can be given the right situation.
If you are going touring I feel you need a high level of self-sufficiency on the bike. Stuff can and does happen, you want to be able to deal with it, rather than being stranded thanks to a mechanical problem.
That aside you want to do your homework when it comes to planning. From choosing your route, to whether you camp or stay in hotels, etc. You want your tour to be within your abilities and comfort level.
There are places around the world (and the USA) I would feel comfortable touring in, and others I would not. That just reflects my own opinions, information, and perhaps, even prejudices. So whether it is because of crime or hostile drivers or seedy surroundings - you have to make that call.
I remember being in Alaska about 6 or 7 years ago in winter . I met this guy at a hostel in the Southeast, (Skagway), who had ridden from Anchorage across to canada, down to the washington state, then caught a ferry/boat up to the peninsula. That's one tour I would not have done for a variety of reasons, but then his perspectives and margin of error were different than mine!
For your first tour, provided you have taken these steps, I'd recommend choosing a well-traveled route at a popular time of year where you would be likely to encounter other cyclists. While you would be out on your own, you'd nominally have other rides to give you a sense of companionship.
BTW....great picture!