With Air Canada i needed to let them know ahead of time and pay 50$, plus bring her in an appropriate carry-on and show up an extra hour early. Security was a breeze (fun, actually, because i carried her through and everyone was way friendlier to me than usual! LOL). I got a glass of ice cubes as soon as i got on each time and let her chew/lick those for hydration. Because i could not leave Toronto airport inbetween the two flights ( no time), i put some paper towel down in the far corner of the handicapped bathroom stall and let her pee on that, then threw it away, cleaned up, and we were good to go again. I would highly recommend going this route if you can. Sure, you can ship a pup cargo - people do it every day, but with all the expense and effort that's going to go into a gundog, it's nice to make sure that they get a low stress start. I could literally see her bonding with me on our first day together on this grand adventure!
There was some paperwork for entering the country, but i'm guessing you're staying within the US so i won't bore you with all that unless you need the info.