If you are thinking of doing a package, room, tickets and/or dinning plan. I would book it all at once, less stress overall. All that calling and changing stuff for me at least adds to more stress. Last but not least by booking all at once you can budget and pay all along, instead of paying all of it at one time.
You will need to decide which plan will work best for your family, with 3 options to choose from, I'm sure you can find something to fit your needs.
I have some friends that did the QSDP route and paid out of pocket for 1 or 2 character meals, and they did breakfast in the room. This worked for them when the kiddos where little, but now they are older they have upgraded to DDP for the last 2 trips again still having some breakfast in room.
DH and I when traveling with family we go the DXDDP route, for us it works out. With character meals, and signature meal, and having everything paid for up front is nice not worrying about who is ordering what, and we can just sit and enjoy the family time. But we are a family that feels that dinning is all part of the vacation experience we want to have.