Very interesting query. I've had plenty of times where people told me I'm like Luna. I love how she always seems to be in her own little world. She certainly sees details that the other characters always gloss over. She's painfully honest without even realizing that most people are uncomfortable with it. Also, she doesn't express much emotion, even though it's clear that she highly values the few friends she has. She's probably ecstatic to be around them, yet she doesn't show it via body language. Not to mention, she couldn't care less for social convention and how she appears to the public. Giant roaring lion hat? What could be wrong with that?
On the other hand, she's not exactly the most logical thinker. She believes many of the stories from The Quibbler. Though it's true, she's heavily influenced by her father, and sometimes his stories do at least have a grain of truth behind them. It's also hard to tell what's logical and what's not in a world where magic exists.
I'm also not sure if she has any special interests. Her love of The Quibbler might, in itself, be a special interest, but is there anything else we've seen her obsess over? Maybe we don't get to see much, since she's usually over in Ravenclaw and we don't get to see her very often. She very well might be going through many special interest cycles when she's not part of the plot...
... Also, you guys may be interested to know that when I type "Does Luna Lovegood" into Google, the third suggestion it gives me is, "Does Luna Lovegood have Asperger's?"