Yeah I don't want to be bursting the bubble on your dreams but you better at least triple that amount. If you have a car assuming you do, your factoring that in hopefully right (gas, insurance, car payment if there is one). If your planning on doing the uber route that gets expensive every day. Food and drink is expensive too and when your saying your getting a roommate is it some random person? or an actual friend you can trust? If its a random person I would scrap the idea of LA.
Utilities add up quick, internet, electric, water, trash, gas (depends what kind of place your at) I say a good rule of thumb is factoring in at least $150 a month at the very least.
Your lucky if you end up finding a 2 bedroom under $1,200 that isn't complete garbage in a crime filled location. Most places require first months rent and some require last months up front as well. You gotta save up more.