Honestly, I would say either have a place to stay in, money for 3 months rent, and ideally maybe even have a job lined up before you go. Key would be knowing where you want to be before you leave. You can job hunt and room hunt before you even live in another state (the joys of phones and email!).
I think you have a very respectable dream to pick up your life and go where you'll be happy
Flip a coin, "do I stay or do I go?" make it a high flip, and as it's in mid-air, what side you hope it lands on is the side you should do regardless of what it lands on, because at that coin starts to fall you realize what you really want to do/want to happen.
save the 9 grand, get a job in flat roofing (I work for 18 bucks an hour with no qualifications) and keep building that nest egg. Ive worked for half a year now and saved 6000 bucks for my education, so it wont take long to get a good sum of money saved up. In that time, you can change a few aspects of your life and plan shit out in the long run
its roofing commercial buildings, with tar and that jazz. and hell, our safety representitive is a chick so its not all that uncommon to have girls in construction. but its just a suggestion, you could get a job anywhere and save up if school isnt going your way. you can always go to school later on
10,000 isn't a lot of money, and this in the hopes you land a job straight away. I wouldn't pack your bags without getting at least 3-5 interviews. Do you have any friends who live there? Maybe you could stop there?