of course it's feasible. i'm sure (90%) girls your age, perhaps younger
have successfully crossed the country by bike.
logistics should not be a problem, especially if you follow established
routes.
your main concern i guess is safety. what can go wrong as you're cycling
alone on an isolated country road? crazy drunk drivers, grizzly bears,
feral dogs or raccoons, crazy dudes with guns, chainsaw guys in hockey
masks, larry the lounge lizard.......
if it's in your budget, have you considered a tour of europe? excellent
transport systems, more of a bike culture, youth hostel network, more
chance of being able to use your student card for discounts, etc.
plenty of challenge........climb the alps! follow the tour de france route,
study a bunch of languages, teach yourself to converse with the locals.