Legally, I think you could do it yourself, however I suggest for your first home & with your only having just obtained your real estate license 2mos ago, you should work with another agent. I see your broker is in Temecula, have you been in Los Angeles very long?
I think you would greatly benefit by allowing another agent to represent you, this way throughout the entire transaction you can learn a great deal about the area, the contracts and each & every step of the process.
I have been a Realtor for 15yrs now, please email me Directly if you'd like to talk to me some more. I don't look back on this same Trulia posting for answers after mine, because it fills up my email inbox.
Realtor Since 1996
Main Street Realtors
Servicing clients within 300mi of where I live successfully!