Legal Question in Family Law in California

You need to go back to the court order re the child custody to find out. Sometimes the order will specify which territory area the child can live. If that is the case, all you need to do is to give notice a certain time before relocation, provided also in the order. If not or you are moving to a county which is not specified in the court order, then you may have to go to court to get a permission.

As it is your ex who has full physical custody, no, you do not need her permission to move as you would not be changing your child's place of residence.

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I would double check the court order. If the order is silent, I'd still advise you to let your ex know of your plans. If she tries to thwart your visitation, you'd have advance notice and some lead time to determine if you need to go back to the judge to protect your visitation rights.