Welcome to the site, "Tawanda".
Side note, if I may:
When I saw your screen name I
instantly thought of one of my favorite scenes in the movie "Fried Green Tomatoes".
Link to clipAny connection? :B
Per your query:
Though married, I've traveled quite a bit on my own with the trailer. Never all the way across the country, though, so can't make any recommendations as to route etc. Most of my travel has been on the west coast, California to Washington State. As a general rule I stay off interstates just because I prefer the more leisurely pace/scenery of secondary roads.
Not sure what questions you may have about solo travel as a female...I will say that I've never felt afraid to be on my own, depending as I do on a well-developed sense of my surroundings when choosing places to stop/camp/whatever.
I boondock almost exclusively, if that's of any interest to you.
Good luck!