Legal Question in Family Law in California

Yes, but you will need the court's consent. If the move will not alter or interfere with the father's custody, the consent will be pretty much automatic. If the father fights it for some reason, there is no way to say how it would turn out without going into all the details. If and when you do move, it would also probably be a good idea to transfer the case to your new state of residence. When neither parent nor the child lives in the state of original filing, it is rarely desirable to keep the case in the old home state.

From your description of the case, it seems that the father's time with the child is impacted by geographical distance in light of the fact father lives in a state other than California. If your planned move will not hamper the existing time share arrangement, I cannot see how the court would not support your relocation to another state.

I should just add that there is no problem with changing counties as long as it doesn't change or interfere with the father's visitation or custodial time.