However strong your feelings may be for this girl, or whatever they're really for, take time to really consider the possibility that you are just trying to navigate your way out of a painful chapter. It doesn't work that way. You will have to feel what you're trying not to feel right now. This girl isn't going to save you or replace what you lost.
I went out several times with a guy going through a divorce so recent I'm not even sure he had finished moving all of his stuff out of their house. When I wasn't listening to him complain about his ex-wife or having some of the worst sex of my life, I was busy debating him on how he wasn't ready to be out in the world, "dating." In my defense he was very handsome and I had a rough idea of what I was in for. I promise you that you are not fooling anyone right now.
For one, the woman is 23 years old. When we're young, we sometimes read train wreck as romantic; delusions as compliments. Please don't attach much to this young thing. It sounds like you see something new and full of hope, and maybe she's the only real bright spot in your life right now (aside from your kid, I guess) which is never good. Even if she is ready to settle down (she's not) into your imaginary world of domestic bliss, she is almost certainly equipped to help you.
Finally, to answer your actual question on tips for how to play it cool: sit this girl down, tell her you're not emotionally ready for this and then leave her alone. It's the coolest thing you can do.
I just started seeing this guy and I'm crazy about him. I also just found out that I'm moving for work to a city six hours away. I don't leave for a few months, should we stop seeing each other? I can't stress to you enough how crazy I am about him.
The easy answer is yes, of course. Cut it off before you're too deeply attached and spare yourself a tearful airport goodbye or doing a big speech about what life could be like, Family Man style.
But if you're like most people, when you like someone in those early infatuation stages, no rhyme or reason is going to keep you apart. It's really the reason most people end up together at all: the total suspension of disbelief. You probably know that the logical thing to do would be to end this, but we both know that's not going to happen. So keep seeing each other as long as you can, be realistic about the situation you two have found yourself in, have a lot of sex while you can, and be prepared to cry at the airport asking, "Why did I do this to myself?" Hey, if this is the guy, who knows, maybe he'll eventually make the move with you. If not, you'll be single in a new city. There are worse things.
If you have questions about relationship etiquette, please send them to Ask Alison [at] The Atlantic (.com).