We rented at Emerald Island with our dog in 2013. It's a good neighbourhood, and as close as any.
At the clubhouse, the receptionist told me they don't take dogs, but in that case the truth of it is that if you rent directly from the resort, those units don't take dogs, but for individual owners (our case), it's up to the owner.
As a pp said, go to VRBO and use pets as a filter. It cuts down your options considerably, but they're there.