Can you work at an airport in a different state?

Yes, it happens all the time. It can be a pain in the neck, though, as it involves a significant commute. Imagine, if you will, that your schedule is four days on, three days off. On two of your three days off, you'd be commuting...First from VA to home, then from home to VA. If it's something you're willing to do, then I say go for it! Just be sure you're understanding the implications before you get into it.