In general you don't want to start post-doc before you get your limited permit. In some settings, such as the VA, you may be allowed to do so by law. However, The state will not count those hours toward licensure. The permit identifies a licensed supervisor and starts the clock on counting your hours. Complete the paperwork as soon as you know where you are going for post-doc. Your supervisor/site should be familiar the process and recent timelines for getting a limited permit approved.