If we agree to change our parenting time schedule, do we have to notify anyone or can we just implement the change ourselves?

Technically, no. No one will know if you both adjust the parenting schedule and implement a different plan than what is in the formal agreement. This works fine when you are getting along.  If there is ever conflict, however, you could potentially be helped to whatever is in the originally filed parenting plan. In order to avoid these types of conflict in the future, it is always advisable to update the parenting plan, either formally or informally if allowed in your jurisdiction, so you have a signed agreement in line with the parenting schedule you are currently implementing.