A conviction for California Penal Code 647.6, misdemeanor child molestation, requires sex offender registration.
A so-called "expungement," which is actually a dismissal under Penal Code 1203.4, will not relieve you of the duty to register... but it is the first step toward a Certificate of Rehabilitation, which will terminate sex offender registration in misdemeanor cases ONLY.
However, to be eligible for a Certificate of Rehabilitation in a 647.6 case, you have to wait ten years from the date you were released from jail on the offense. You can apply for a 1203.4 dismissal now, as long as you have completed probation.
Although 1203.4 dismissals are often called expungements, they do not really expunge anything. They just add a notation to the court's public record that the case was dismissed. You still have to disclose the conviction when applying for any sort of state license or job, and it specifically will NOT relieve you of the duty to register as a sex offender.