Can I take my child out of state?
A holiday and a move are completely different questions. Traveling out of state for a week is normally fine, often with notice to the other parent. Relocating is a major change that usually requires their agreement or a court's permission, and doing it without either is one of the most damaging mistakes available in a custody case.
Start by working out which one you are asking about, because people search for them in the same words and the answers are nothing alike.
Traveling
Read your order first. Many parenting plans address travel directly: how much notice, whether you must share an itinerary, whether written consent is needed, who holds the passports. If yours says something, that is your answer.
If it says nothing, the practical approach is to give written notice well ahead with dates, destination, and where you can be reached, and to keep it to your own parenting time. Most disputes here come from surprise rather than distance.
For international travel, check the passport requirements early. Applications for a child under 16 often need both parents' consent, and this is a slow thing to discover late. Not always, though: if you have a court order giving you sole legal custody, or the birth certificate lists you as the only parent, you can apply on your own, and nobody should send you looking for a signature you should not have to ask for.
Moving
This is the serious one. Relocation is the fight that reopens settled custody cases more than any other, and the wrong sequence causes lasting damage.
Do not move first and ask afterward. A parent who relocates with the children without consent or permission can be ordered to return them, can lose credibility that colors everything else in the case, and can find the schedule reshaped in ways they did not anticipate. Whatever the merits of your reasons, moving first turns a discussion about the children into a discussion about your conduct.
Many states require notice before a relocation, and where notice is required it usually runs 30 to 90 days with specific contents, and many require agreement or a court's approval where it would substantially affect the other parent's time. Distance thresholds and procedures vary considerably.
Courts weigh whether the move serves the child, not only whether it suits the moving parent. Better job, closer family, and a genuine improvement in the child's circumstances are the kinds of reasons that carry weight, and a workable plan for preserving the other parent's relationship carries more than most people expect. Proposing longer summers, covering travel costs, and building in regular contact is often what turns a contested relocation into an agreed one.
If there is no order yet
You may have more freedom, and less protection than you think. Moving before anything is filed can still be held against you later, and it can affect which state hears the case, which is consequential in itself. If a divorce is coming and you are contemplating a move, that is worth advice before rather than after.
The exception
If you are leaving because you are not safe, the rules above are not the first consideration and there are procedures for exactly that situation. You do not have to live somewhere for months before that state's courts can help you: a court in the state where your child actually is can make emergency custody orders right away when a child, a brother or sister, or you are being hurt or threatened. It should still go through a court rather than a unilateral decision wherever possible, and an advocate can help you plan it. The safety resources page has the numbers.
Notice requirements, distance thresholds, and the standard a court applies to relocation vary substantially by state, and this is an area where getting the sequence wrong is expensive. Talk to a licensed family-law attorney where your order was made before you move or agree to one.