You do not need to be unemployed to qualify for the Public defender services. You however may need to pay for their services after your case is closed but that will depend on your financial ability to pay.
You don't need to be employed. Whether or not you qualify is another story. I'd call the public defender's office now to inquire. but in all likelihood, you may have to wait until your court date to fill out the application paperwork. Good luck.
Every county is different in terms of what is considered indigent in order to qualify for the public defender. Some counties like Sacramento generally do not as to one's financial status and just appoint the PD except in DUI cases. In other counties, they make you fill out a financial declaration signed under penalty of perjury as to your income. I would say if you bring home less than $1,000 gross income a month you would qualify. If you bring home more than that, then they might ask about your obligations - food, rent, car payment, electric and gas bills and if you support anyone other than yourself.