Got married just before going to Ramstein, and got a dog (practice kid) shortly afterward. Wouldn't change a thing if I could.
As mentioned, dogs are almost universally welcomed all over Germany and we never had an issue with our Westie. In fact, he used to love meeting cows along walks between villages.
As for cars, you can bring a US one over without much problem but understand Germany roads tend to be narrower than in the US (especially older ones). Not sure if I'd bring a F-350 but I've seen people do so.
I bought a hoopty German-specs BMW 3-series from a Lt Col for about $1500 when I got there in 1995, I'm sure it's still easy finding a second car at a decent price. We kept USAA insurance during our time there.
I hope she enjoys GK, it's in a great location if you like rural environments! The biggest issue is the limited US services provided. I believe they send everyone to Spang (a two-hour drive) or Ramstein (three hours).