Yes, you can move out of county. I don't think there is any hard and fast rule of how many days you have, but ideally, you should notify probation before you move or immediately after. Good luck to you.
Many times the court will specify the amount of time within which you need to notify probation or the court if you change addresses. Check your minute order. If not, a reasonable time will suffice, usually within a week to 10 days..
Although a week or ten days does seem reasonable you already know where you are going so why not notify the Court now that as of 1/1/12 your address will be such and such? Why risk missing an important mailing between 1/1/12 and 1/10/12?