I usually stay away from threads like this, but I'm cranky today.
Way back in 1987 my dad took us on a spur-of-the-moment trip to WDW. I was 15, my brother was 12, and my half-brother and half-sister were 3 and 4. I think, at the time, 3 and under were free and 4-11 was a child in Disney's eyes.
So we get to the gate to buy tickets into MK (they hadn't heard of planning). And my step-mother decides that this is way too expensive. I'm instructed to "just stand away from the ticket window and look young." And they proceed to buy child admissions for my brother and I and the little ones sail in for free.
I was furious and humiliated. I was 15, had a boyfriend at home, and was expected to pay for all my own "extras", up to and including sodas and treats, with the money I'd saved from my part-time job. We also went to Wet 'n' Wild and Medieval Nights and the entire trip was one of "god, this is so expensive, just say you're *this age*" or whatever age was the cutoff.
The little ones don't remember the trip at all. Most of what I remember is that my step-mother was more concerned about what having ME along was costing her. Plus, I was terrified that someone was going "catch us" if I suddenly looked too old, and that they would throw us out of the park. Plus, the "furious and humiliated" part tends to stick with me too. Seriously, at the time, I think I would have preferred to stay home.
The irony is that two years before, my aunt had taken me and happily paid the right price. And it was a much happier trip.
I'm assuming you mention the speech delay not to justify what you might choose, but as evidence that you probably could get away with it. And, as others have pointed out, you probably could. After all, at 15, they passed me for 11.
Just like I could probably get away with paying the child rate for my daughter who will turn 10 exactly 30 days before we go. She still LOOKS like a nine year old, right? And it's not like the number of attractions she can access/enjoy is going to change in thirty days.
But.
We'll happily pay the price. Visiting Disney is not a need, as much as some of us here (me included!) sometimes act like it is. It's a vacation that we're grateful to be able to choose to make. When we plan our trips, we choose when to go and who to bring, knowing what it's going to cost. For the next trip, accomodating the increase means we'll stay a day or two less. We could just as easily have chosen to go a month earlier, or waited another year until the oldest girl was off at college. (which would have been cheaper still, as we're the Family Of Five who also won't try to "sneak" us all into one room.)
Your choices are your choices. Pay for the ticket or lie about her age. Every choice has consequences though, and sometimes they're not always visible, immediate consequences.