Hi,

What do you feel about her? is the real question.

If you are attracted to her physically, then yes go ahead and suggest to see her outside work.
If you are attracted to her personality, then yes go ahead and suggest to see her outside work.
If you want a bit of romance (that help after an LTR break up), then yes go ahead and suggest to see her outside work.

I would suggest that if you start seeing her outside work you should keep some distance at work. That's my opinion.