AREX Express to KTX for Busan with Cat?

I’ll be moving to Busan for my job, but unfortunately I cannot fly directly to Busan as I’ll have my cat with me and he has to go through Quarantine at Incheon. I was wondering if anyone knows if I can take him onto the AREX Express train(and all of my luggage) to Seoul Station, and then on the KTX train to Busan with him as well(and also all of my luggage). My only other option would be to catch another flight at the Gimpo airport to Busan but I haven’t even began to look into how to get over there.

Thank you in advance!