We moved overseas a year ago and Ruxin came with us. Figuring out how to get him here was nerve-wracking to say the least. Unfortunately, he was too big to fly in cabin with us and had to go as checked baggage.
The recommendations are great, but please check each airlines website to read their rules, as they all vary and are subject to change. Make sure your carrier fits the dimensions specified by whichever airline you decide to go with. Your dog should be able to both lie down and stand up with enough room, ie feet not going over the edges, head not hitting the top.
I'm in a Facebook group for flying pets so I see questions like this very frequently! Some airlines do have age restrictions, FYI! Pretty sure I'm giving you more info than you need, but I'm used to international flights and all the fun stuff that comes with that. Good luck!