Is it really the only thing she wants in the entire world?
That is what she's trying to sell you, and you seem to believe her. So does this mean after she gets it she won't ask for anything else, ever? (Or at least for the next few months?)

I think I might have heard those words a few times before...
Personally, I would ask my DD to put more on her list for Santa, or else knowing my DD, I would get her some really great gits that she could enjoy after getting over the disappointment of not having an iPhone. Just as you have the attitude that binkies aren't for 3 year olds, I have the attitude that these kind of electronic devices aren't for preschoolers. But, I know many people disagree and that is fine-- it comes down to what your beliefs about this are, and as long as you do have some kind of limits that you set regularly, it's not the end of the world. Who doesn't want to make their kid's face light up on Christmas morning?
It also sounds like maybe you have older kids to consider...what would their expectations be, seeing this gift (or what would your DD's expectations be for future Christmases), or do you have a firm understanding that the big ticket item comes only the year you give up your binky?