Welcome to the Disney Parks Moms Panel, Morgan!
Your question brings back such fond memories for me. When my husband and I took our son for his first trip to Walt Disney World Resort, he was five years old. He was a tall kid who rarely used a stroller in his everyday life but I had a feeling that he would be glad to have access to his stroller in the airport and in the theme parks. My husband thought taking his stroller would not be necessary. He's a wise man so he relented to his wife's plan and we took the stroller. Boy, were we glad we did!
Walt Disney World Resort vacations are exhilarating, fun and exhausting...especially for little ones. Guests do so much walking in the theme parks and at the hotels. Now imagine how many more steps preschoolers and toddlers have to take to cover the same ground. Both of your children will be relieved to have access to a comfortable seat now and again during your vacation. You don't need a fancy, bulky stroller; a lightweight umbrella stroller would be just fine. I would advise against wearing your younger child. It is still pretty warm in September. You'll be much more comfortable with your little one in a stroller.
If you think that one stroller would be all you need, you could always bring one stroller and leave open the option of
renting a second stroller if you find you'd like to have one. Personally, I'd bring two lightweight strollers for optimum mobility.
No matter what you decide, cherish every moment with your children on this trip. I get a little misty-eyed as I think about my son's first trip to Walt Disney World Resort. I remember that trip as if it were yesterday, and yet he'll be off to college at this time next month. So, take lots of pictures, hug plenty of characters and keep a journal of all the magic you experience together.
Sending best wishes and pixie dust,
Jill