I would also recommend looking at the plane seating chart to see where your seats are and where the exit rows are.
We made the mistake of booking with American online when my son was 4 months - I booked our seats so that we would be sitting in the 2nd row behind the exit row. When we arrived at the airport, the agent told us that she could not allow us to sit in that row since we had a infant carrier / carseat. American does not allow carseats/ infant carriers, etc to be 2 rows in front of or 2 rows behind an exit row. The flight was oversold, so she was going to have to split us up. I totally freaked out.....here I had bought my tickets 6 months ahead of time, purchasing a ticket for my 4 month old, which I input on American's system that he was an infant and their system allowed me to book the seats there. I had no idea this was their policy. She ended up getting us all together, but we had to do the whole check in at the gate thing and the agents there had to work to get us all together. We also had the same problem coming home - which they could not fix that day, we had to wait until day of departure.
So check with Delta and save yourself a nervous breakdown at the airport!!
Also, I notice you are in TX....we fly out of DFW, don't know what airport you'll be flying out of. 6 am or before can surprisingly be busy at DFW....lots of business people flying out in the early AM. My hubby HATES getting to the airport early, but I would rather get there early and breeze through security with no lines, especially juggling young children, snacks, carseats, strollers, etc! Then you can sit down at your gate, collect your thoughts and make sure you have everything.
I let my youngest walk up and down in front of the stores to get the wiggles out before having to sit so long. Its also great time to get some extra water or juice for the flight.
We always pack a carryon suitcase with our DisneyWorld snacks - its actually my DD's little Tinkerbell rolling suitcase we bought at WDW. It fits perfectly in the overhead or on the floor under the seat. I just always put my stuff in ziploc baggies just to be on the safe side. Then you can always use the empty baggies at WDW for something. Last year we took those "little boxes" of Kelloggs cereal, Nutrigrain bars, bags of goldfish, "fun fruits", etc. We had no problems or questions for bringing food through security, so you should be fine.
My DD always wants to EAT once we get to the gate, but I make her and DS wait until we get on the plane. It gives my DS something to do on the plane and occupies him for a little bit before I have to start pulling the "plane surprises" out to keep him quiet!
Have a wonderful trip with your family - noticed it was your 1st - it will be magical!!
Wendy