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Your description of your Dream Girl makes both of you sound like L. L. Bean models - beautiful, perfect, smug, smart, thoughtful, utterly self-absorbed, but happy to spray a little false modesty around when you realize it would help your images.
In other words, you're both about, what? Twelve?
Kids will mature you, that's for sure. Kids will expand you beyond all reason, or belief. I think you should have them - I think you're about ready to move away from the relentlessly smug narcissism that's run your life so far.
I'm not sure Piper is, though. Has she matured at all past that nauseating, cutesy-poo description of her? If she hasn't, then the two of you are heading in different directions, and you need to jump ship. Dream Girls who don't mature past the Dream Girl stage are death to the soul in middle age, both theirs and yours.
Up to you. Piper sounds like she doesn't even want to deal with a puppy, and that's usually the first step that L. L. Bean-drenched couples take.
Get real, guy. That's all you've got left, with kids or without.