My DD's last trip nursing was when she was 18.5 months old. Your lucky your's isn't distractable. Mine was, so we needed a quieter place to take care of business. No way was she going to nurse on the rides or at the shows at that point. I think I tried to nurse her at the American Experience show and she was even interested in watching that.
She wasn't nursing a ton at that point. Morning, night, and a couple of times during the day. However, at WDW she definitely nursed more than at home. I used the Baby Care Centers a fair amount because they were quiet and dark which was good if I was trying to get her to take a nap. We are into park hopping, so one of the best places for us to nurse was the Friendship boats from MGM to Epcot. It's about a 20 or 30 minute ride, so she had plenty of time without me needing to move. I would think the monorail ride from the TTC to Epcot would be another nice place to nurse. It's air conditioned. I was always able to find some quiet benches in the World Showcase to sit down at.
My DD had three trips to WDW while she was nursing (she nursed for 22 months), two of which when she was a toddler. I agree with GEM that nobody really bats an eye at it. You will probably experience far more criticism here (see the nursing toddler thread that was bumped up today) than at the parks. I talked with several moms of infants in the nursing rooms about nursing a toddler on our trip when she was 18.5 months old and they seemed genuinely interested in the subject (questions like how many times a day does a toddler nurse, etc.). They did not give me the feeling that they thought it was strange or anything.
) she loves her boo-boos. I have drastically decreased our NIP since she turned 18m, but I doubt she can go all day without nursing.
Now when she wants just a sip here and there its a different story. I will do a search for nursing here on this board 
