Leila,
Whatever tips you garner from all these experiences solo riders/adventurers, be forewarned that you cannot give your parents peace of mind! When I was young, I headed west by myself in my car, camping along the way, and there was nothing that could convince my parents I would be safe. After I arrived safely in Phoenix and made my home here, they still worried. Worrying is a parent's job! My parents are gone now, but I have a husband who worries about me when I head off on a bike adventure. I think it's a matter of preparing for possible complications, and then just going for it.
I'm sure you'll have a blast preparing for the trip, dreaming about it, and then living it. Good luck! Please keep us informed about how it's going!
Jan