You probably won't be able to do it without an "in", so to speak. A friend or acquaintance that lets you live with them until you find a job that pays well enough to live. And you'll not only need that support, you'll need at the bare minimum 6 months of rent, expenses, etc. saved up.
A few years ago, I did the same. I moved here because I wanted to be in Austin. I didn't know anyone, lived in a Super 8 motel, eventually convinced some wacko to let me rent a room month-to-month in his sketchy drug-haven condo until after 5 and 1/2 months and -$10,000 later, I found a living-wage job in my field and got out into my own place. Now, I have an awesome place in an awesome neighborhood and I'm absolutely 100% glad I did what I did, but in retrospect it was a stupid gamble that could have ended with me just losing all that money and time and not making it.
Now, I was a guy in my 20's and an athletic 210 lbs. at that. My meth-addicted roommate may have terrified me with his tweakage, sketchy friends, and weird homicide fantasies, but I scared him too because I'm intimidating. A 19 year old girl will not be so lucky...and if you end up like me where a normal seeming potential roommate turns out to be a closet meth-head who physically threatens you, and he has power over you because he gives you housing without a lease, you might find yourself face-to-face with his dirty crotch on the regular. My old roommate peed on a drugged up girl in our shower once.
Unfortunately, Austin is just full of these drugged-out sketchy dudes (mostly from California). I was appalled by the number of people who live here that are completely drunk or on drugs all the time. Meth is everywhere, so is coke (for the richer ones).
One thing that will get you here is the fact that, unlike most of the north east, the vast majority of rentals and leases require proof of not only lengthy (6+ months is typical) employment but a salary that is at least 3 times the monthly rent. If you want to rent for $600, you'll need a full time $10/hour job at least.