Can I get a rally license when I get to the rally?
Usually, yes. But we really don't recommend that. Why? Because on your first rally, you're going to have plenty of other things that are keeping you busy. Filling out paperwork and medical forms, remembering who your physician is and what their contact info is.... really, just don't do it.
Think of it this way: you can either do this at home one night, leisurely, with all your computer and internet resources available, with time to spare and contacts to find answers to questions... or you can do this not during business hours, when everything is closed, you don't have cell service, there's no wifi, and when you're on a very tight deadline to be somewhere else, and you have a few more things to fix on the rally car before starting, and you got there late because it took longer than you expected to pack and prep to leave for your first rally.
What people imagine is "Oh, it will be easier because there are people there I can talk to if I have questions." However, the reality is "it will be more painful because by the time I finally make it to the rally, my very limited time will want to be spent doing something else."
So, to make it easy on yourself, get your license and membership straightened out about a month prior to the rally. Especially your first one. Also, please consider that the folks staffing registration are volunteers and it's more courteous of you to not make them work harder because you put off handing the paperwork that you would ultimately have to do anyway. :)