If I’m currently married but seperated and there is no parenting plan, can I move out of state?

If there is no parenting plan, then you can technically go wherever you please because you have full custody rights to your children--but so does your spouse, so s/he could file any time and force you to come back to deal with the case (potentially just as needed, which might not be a big deal if your new state is nearby, but it's also possible that the court could order you to return the children as well pending a final decision).  Washington will retain jurisidction so long as it is the child's home state, which can be defined by a number of different criteria (see the UCCJEA), but it is typically wherever the children have lived for the past 6 months.  If you live with the children for 6 months in another state, you could run into a lot of trouble because that new state will have jurisdiction over the children but not over your spouse (so it wouldn't be able to require the spouse to pay any debts or divide property here in WA).  It would likely be least complicated to get everything settled before you move, but either way you should discuss the specific facts with an attorney before making any decisions--a lot more goes into multijurisdictional divorce/custody cases than can be adequately addressed in an online forum.