Book early. Repeat: Book. Early.
I’m notoriously bad at booking my flights early. It’s just so much commitment, how do I know what will happen in six months?!
This all changes when you have a dog, because if you don’t do this, you may not be able to fly AT ALL. I’ve taken the risk and almost missed a friend's wedding. I don’t recommend it.
Almost every airline has a limit on the number of canines that can fly on a plane at once, and it’s shockingly low (like, 2). No, I don’t know why this is; yes, I think it’s weird, too.
But since alerting them to this won’t help your case (I’ve tried!), booking early is essential -- your dog must be locked into one of those exclusive spots. When you book, make sure to check the “traveling with a pet” option. Don't forget. Oh, and this “luggage” will cost you far more than the checked variety. Standard rates for flying a carry-on dog are about $150 each way.
But wait, there is a loophole (and one that's being abused more and more these days): it’s called registering your dog as an Emotional Support Animal, and it means you never, ever have to book or even pay for your dog to fly. It does require some physician-signed paperwork, however. And not the kind you forged to get out of gym class.