Olivia,
I think your plan is fine. You have a nice share of each park, with an appropriately higher amount of time at the Magic Kingdom. This is essential with a 5 year old!
The only thing I noticed is that you are not getting to take advantage of many of the Extra Magic Hours. Of course the October Extra Magic Hours have not yet been officially published, so you might have a few, but I doubt it.
If you already had these Advanced Dining Reservations set then I would not recommend changing them just to get some Extra Magic Hours. But if they had yet to be made, and you wanted some advice on how to shuffle your days to get more park time, I would say to do it this way;
- September 27 - Magic Kingdom
- September 28 - Epcot
- September 29 - Hollywood Studios
- September 30 - Animal Kingdom
- October 1 - Magic Kingdom
- October 2 - Park of Choice
- October 3 - Magic Kingdom
As I said, however, your initial plan is very solid. This second schedule idea will just get you a few extra hours in some of the parks.
Have a magical vacation!