I would say this is not very possible....if you have your heart set on acute care and pediatrics. Nowadays, most new graduates get jobs in hospitals via a new grad program, and it is at hospitals they did clinical/preceptorship while in nursing school. And the hospitals in my area DO NOT accept new graduates into specialties like labor/delivery, peds, ICU, OR, ER. You first have to work in med/surg, ortho, neuro for a year and then transfer over or apply for a training program. Southern California has more facilities, but also more competition and lower pay.
However, I do see a lot of jobs for a pediatric home health nurse and they train new graduates. However the pay is extremely low, I mean extremely. People in Starbucks probably make more. In my area, they start out at $18/hr, but considering new graduates in a hospital start at $50+, this is nothing.
If I were you, I would stay put, gain experience and then come to California. After you have the experience, particularly in a specialty, many hospitals will pay a bonus and sometimes even relocation benefits.