The 3YO I would either dress in comfy travel clothes the night before and let him sleep in those or keep him in his PJs and not change him until you are at the gate. I think the 9YO and 7YO will be able to dress in the morning provided you have clothes all laid out the night before.
* tell them you plan on them sleeping in the car on the way to the airport. Don't bother with breakfast at home that early. You've set the expectation that there will be no bowls of fruit loops so hopefully can avoid any meltdowns caused by breakfast expectations.
* bring some snacks in case they are bright-eyed and bushy-tailed. Bagels, bags of dry cheerios, yogurt tubes they can suck down before security. Keep some snacks for the plane. You can plan on grabbing breakfast at the airport too.
* I'd wake them 15-20 minutes before you need to leave. That gives them enough time to go to the bathroom, quick brush of the teeth, and dress before you head out.
* do everything else you need to BEFORE you wake them up. Finish the suitcases, pack the car, final instructions for any neighbor or house/pet sitter, etc. While one parent is getting the kids ready, the other should be canvassing the house for any forgotten items and checking that things are turned off, unplugged, locked, etc.