All others have already said this but yes, pets on the reservation can wreak havoc with the online system. Then again, sometimes it works out just fine, so who knows. I would also recommend calling to try and straighten this out (and reconfirm your dog reservation, while you're at it).

Note that refaring your itin will cause you to lose your pet reservation, so if you want to refare, call and make sure they preserve the pet space.

Pet reservations are actually always one-way... you have to ask for each way when you fly with a pet, which is part of what makes flying with an in-cabin pet somewhat difficult.