This sounds promising for you but before she puts you in the friends category, you better hurry up your game before another guy puts some moves on her! Call her and ask her on an actual date. Use the word "date" in your phone request. You ask her when you will pick her up for the date and arrive on time. Dress up a little for the occasion - just enough so she knows you made an effort (not a tux unless you're going to a formal ball). Think Dockers, not jeans. Think collared shirt, not t-shirt. You show up for the date with a rose or bunch of flowers, you take her to the date location, and you pay for everything. You hold open the doors for her while on the date, help her with her sweater or coat, etc. You kiss her at some point or have a good night kiss at her door. Now THAT'S a date.
Just hanging out and having dinner together is NOT a date. Asking her just to dinner is too vague. I go to dinner all the time with my guy friends and it means nothing... and yes, we laugh and hang out for 2-3 hours each time - but I date someone else and they are clear they are nothing more than friends to me! Be clearer in your communication and you'll know where you stand with her.
It takes a bit of guts to ask her out on a true date but it's better to know where this is going. If she says she's dating someone else or "just started" dating someone else or not dating at all, then you know you're out of the running as a romantic partner. If you value the friendship you started with her and can handle just staying friends, then keep her as a friend. Feelings can change over time for women once they know a man very well.
You sound like a good guy. Good luck!