My ERGO is khaki, the lightest color they have, but it was WAY to hot to use at WDW in early fall. Taking it on and off to cool down was a major pain, so after the first day I left it in our room and stuck to my sling for the rest of the trip. (With a 10 wk old in Sept; exact scenario as the OP.)
RING SLING. Preferably light-colored mesh at that time of year. You can use it in several different configurations if you buy a bit of extra length. The tail acts as a sunshade and provides nursing privacy as well. (FWIW, IME the best outfit for nursing in the parks is a stretchy tank top under an open short-sleeved shirt; pull the tank inward from the armhole.).
I did five different trips with kids under 8 months: the ring sling was the best option, hands down, because it was much cooler to wear, compact to store, and easy to take off and on.