While the connection should be doable, I would recommend holding off on any shopping or dining until you get to the Iberia gate just to be on the safe side.
You'll be arriving at gate D53, D55, or D60 and you'll have to walk to the automated people mover station on the fourth level of Concourse E, then take the train to the international satellite terminal where your Iberia flight will depart from gate E23. I would time it at about 20 minutes. Taking the skytrain to get from the American Eagle gates to the Concourse D-E connector isn't really worth it since you'll lose more time going up and downstairs and waiting for the train than it'll save you, but the train between the main terminal and the E satellite is the only way to get there.