I love Rose in the first spot! It is sweet and simple. Also, the last time it ranked in the top 100 was 1960, so I think it's far from ordinary, at least as a first name. She might have a couple classmates with Rose as their middle name, but odds are she'll be the only Rose/Rosie.
Rose Elizabeth (the first that came to mind. Very classic, but perhaps you want a bit more oomph?)
My SO loves the name Rosie for a girl. While I love Rose for a girl too (mainly because of the Titanic movie), but I would never actually want to use it. But it is a gorgeous name! Its so simpleand elegant!
I love Rose in the first spot! I know an adorable 3 year old Rose - she's seriously one of the cutest kids I've ever seen and she wears the name easily and well!
Sorry for any repeats -
Rose is a timeless classic. It feels common because it is sometimes used as a filler middle, but I don't really know of many people with the name Rose. And yes, Rosie is such a sweet nn. One thing to remember is that while we talk about fn/mn/ln combos a lot here, in the real world, she'll most often be known by her fn or fn/ln, so if the fn/ln choppiness bothers you, just remember she'll be using fn most, then fn/ln, and occasionally fn/mn/ln.
There are lots of names that have "rose" in it that can make your little Rosie stand out! I absolutely love the nickname Rosie
Bellerose - love!
Rosanna - love!
Rosemary - love love!
Rosabeth - love!
Names that mean rose or have flower connotations (and you could still call her Rosie, because why not? It's your damn baby, haha!):
Lita (You could even do Rosalita, which would mean "rose garden".)
Rose is wonderful! I like, as you said, Rose Elinor (or Eleanor). But really, you could pick almost any middle name to go with Rose.