Confuzzled, DGP is right. I'm further along in my relationship and I'm also a woman so I see the headship issue more from the viewpoint of how it would affect you.
Let me be clear: it infuriates me and there is ZERO chance that I would ever abide by a headship rule that is so obviously BS and not actually scripturally based. It was created because it suited the needs of the org. Look up the history of Russell and his wife who helped found the org and what happened when she stepped out of line. But I digress and I have a couple of points to make:
1. The problem is not that you as a nonJW will have to follow their headship rules (although they'll expect you to), but rather that HE will get a lot of flack from the congregation for not keeping you and his house in order. That includes any stepchildren, aka, your daughter.
2. DGP and GaryNeal, because they are males, have an advantage thanks to the JW headship rule in that they could mandate celebrations, holidays, possibly church attendance, etc. Their mates can hide behind that if they didn't really want to abandon all the nonJW traditions. Your man will either have to refuse to do any of that with you or your daughter (or try to prevent you from doing them too!), drop the religion (which you can see is not easily happening) or be seen as a weak JW and possibly face punishment if he's baptised.
3. I have found it pointless to discuss doctrine. They will have an answer or will cling to what they've been taught. Half the JWs I don't even think pay attention to doctrine they're taught until they want out of the religion or unless they were an elder or something that had to pay close attention and the GB introduced some BIG change. You might instead show some of the controversies they've been involved in like the pedofile problem (though, tread lightly, no one likes being called a pedofile!), but there are some articles on it from major news organizations that he might be receptive to. Others can tell you more controversies.
But as the others have said, before he's ready to hear it, he simply won't. That is why it's CRITICAL to take it slow. There is NO reason to get married anytime soon. And when someone else said you need to ask yourself if you can do this the rest of your life, you need to seriously think about that. THE REST OF YOUR LIFE is a long time. I'm not trying to be a Debbie Downer, but in the exciting days of love and infatuation, it's easy to think that all of it's doable and to not want to do it makes you selfish and shallow. It doesn't. It's not just religion, it's a whole culture. And if you take your time with this relationship, you can see how/if you can or would want to do it.
I am glad you refuse to talk to others. That is just so weird! And again, I don't know why they all try to get you to talk to others. Like they're bringing out their all-stars.