Just take KTX from Incheon Airport to Busan. I checked KE.com randomly, and it looks like the shortest layover is like 2 hours and 20 minutes PLUS the hour flight.
Incheon Airport to Busan is 3 hours by KTX train, no need to transfer anywhere or anything. It's a new extension.
Plus, if you're arriving at Gimhae Airport, that's another 30-45 minutes local subway or taxi to downtown Busan. You'll definitely save time with KTX. And, after 15 hours on a plane, it's not another one to sit on.