This sounds like it might be similar to what i am going through right now. I'm very, very fresh to the idea of being single (16 days as of 8:00 tonight), but the desire to have a pleasant, not aggressive, non-painful conversation with someone, to be able to flirt and enjoy their company, etc sounds very, very appealing.
The advice that I have consistently gotten is to be very, very careful for a few reasons.
First, I've been warned that i will have a tendency to jump in headfirst. I can totally see that happening, and that is not terribly healthy.
Second, you (and I) need time to figure out who we are again outside of our marriages/relationships. I don't know how long you've been separated, but for me, it's super fresh after 17 years of marriage. If you go into a relationship right now, you won't be bringing your A-game, you'll be bringing a partial game, a partial person to the mix.
third, considering those first two points, you need to be careful for her sake. If she is a nice person, which I am assuming she is, then you don't want to drop a truckload of baggage onto her doorstep. That could have multiple consequences, such as chasing her away when a bit of time could have made for a much better outcome, changing your codependency from your ex to her (most men (and many women) are very codependent in relationships due to multiple factors) without dealing with it first, and on and on and on.
I'm not saying to cut off contact, but make sure you recognize whether or not you're barreling into her with the desperation of someone who has been deeply, deeply hurt.
At this point, for myself, the ONLY thing I am open to is NSA dates, casual dating, and maybe a careful fling here or there. Nothing serious, nothing long term, just two people enjoying each other for who they are in the moment. Total honesty about the situation and where you are in it. If some chemistry works, great. If not, no hard feelings, no strings.
I wish you luck and healing.