I suppose it depends on how your double stroller folds up but I can't see why there would be a problem with it. I have only travelled with a single stroller (Maclaren Quest).I can't really see why a double stroller would be any different. You will get to board the plane before the other passengers (after the premier class passengers). Both at Dublin airport and Orlando airport we have just folded it up at the gate and left it on the ground where it was put into the cargo hold from the gate. Your flight departs very earlier in the morning, so with two small kids you will really need it. You could check with your airline and ask them if there would be a problem checking a double stroller at the gate. Hope it works out, have a great time at Disney!