Put yourself in that position (assuming you are a financially responsible adult!
). Would you agree to terms like 3 months up front + security deposit? I would. I'd know I'd eff'd up pretty badly and I'd have to suck it up and deal with things like a large security deposit.
If you doubt her income, ask her for pay stubs, or if she's self-employed, tax mailings.
If she balks on any of this, chances are she's full of BS. Not worth your time. Especially if it came through craigslist, the home of the flake.