Hey, congratulations on your little one, and on breastfeeding him!
By federal law, you have the protected right to nurse your baby wherever you wish. You also don't need to take any extra measures to cover up that cause you an undue burden. But if you really want one, be aware that many babies find covers intolerable, so you might want to practice with a blanket or similar thing just to see if he is okay with it. And speaking of blankets, you might find that a blanket, laid over your shoulder, is all you need, anyway. I personally wouldn't bother. People don't have to look if htey don't want to. And a nursing cover is just one more thing to buy. It's marketed so cleverly but is a made-up expense, if you ask me.
If it were me, I'd double up on functionality, as in getting a couple of nursing shirts from motherwear.com (they're having a big sale on their winter clothes now, which is especially great because many of their winter items are lighter and perfectly great for spring). They minimize visibility very nicely while giving you all the access you need (I recommend all of their access options except front-only and all-around-access-only; side-access, cross-wrap, empire, and the others are really great).
The most helpful thing for covering up that I think I can leave you with is, you can get an Ergo carrier, which is especially great for travel, because if you won't be buying his own plane seat with car seat strapped in, you want your son to be absolutely secure in any unexpected turbulence. The Ergo keeps him right near your heart and he will be able to nurse right there without anyone seeing. It's also marvelous for indoor and out-and-about hands-free baby carrying, for helping him get to sleep on particularly tough days, and calming him when he's stressed.
Good luck with your move. And enjoy the extra help from family. I'm jealous!
L.