La Brea Bakery is a great option. My sisters grabbed coffee there before we did rope drop so they were definately open at 7. Not sure how much earlier.
Yes, Catal has breakfast though it wasn't especially quick.
La Brea Bakery has the quick bakey/coffee side and the sit down table service side. I've done the latter and it was good and fairly fast until we were ready to go and had a hard time finding our server to get our check and pay. Could have been a fluke tho.
There's also Jamba Juice (which of course has oatmeal and other goodies in addition to the smoothies).
On our last two trips, Jamba was open an hour before the parks opened (7:00) and La Brea opened at the time the park opened (8:00). On the day of the half marathon on LD weekend Jamba was open at 6 but I think that was a one time thing bc of the race. When we go to EMH that starts at 7:00, there is nothing open in DTD, so we order room service to be delivered at 6:00 and graze while we get ready.
Depends on what you want. For real quick, just grab a bag of beignets from the Jazz Kitchen. They are usually sitting there ready for purchase. Eat them on the way to the gates, but they can be messy...