Hi, Diana! I really think you will need a stroller for your 6 year old. You will be walking several miles each day, and in that hot July sun, a break in a stroller will really help. I would go to a local discount store and pick-up an inexpensive umbrella stroller (preferably one with a top/sun shade.) If there is a small basket for storing your water bottles, sunscreen, etc, that would be even better!
Especially in a park like Epcot that has very little shade and tons of walking, I think you will be happy to have a stroller. Strollers do need to be folded up when entering the buses, so be ready to collapse it when you are boarding.
If you do not bring a stroller from home, they can be
rented or you can purchase a stroller for about $50 in several gift shop locations.
Whatever you decide, prepare for heat with sunscreen, hats or visors, refillable water bottles, wet wipes, and sunglasses. Also plan to take afternoon breaks at your resort pool to cool off! Enjoy your summer vacation in WDW!