Do you just work in the same building or do you sometimes have to work together? If it's the second one, it might be a good idea to keep things on the friendship level for as long as you possibly can. If you date and it doesn't work out, it can make the work situation really complicated.
I think if your going out of the way to compliment and ask her out to dinner, she's probably picked up on the fact that you like her. It's a little more than just a friend situation. But you also haven't necessarily confirmed that it would be a date. I think if you want to make sure she'd be okay with that, you should just ask her, "Do you mind if I make this a proper date and pay for your meal?" I don't see any point to being subtle and beating around the bush if you want to be dating her.
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy