I like the Doubletree because, although a notch below in terms of hotel "stars", it is an all-suite hotel. So if your daughter needs to get a nap, she can be in a room with the door shut, and you can have the tv and lights on. Also, you get a little fridge, microwave, and coffee maker. You can walk to Gooding's if you want (very overpriced but convenient grocery store).
I would't rely on their transportation; I'd drive a car.
If extra magic hours are important to you, you have to go with the Hilton. With little ones, that never mattered to us, as we'd be sound asleep so early! We're so boring, but proud of it.
Either way, I'd use a rental car, or if you're at the Hilton, get to DTD and use Disney's busses. But I think driving is faster.
HTH