Stick to the determination not to have another child. YOU feel complete with two. When one partner wants another kid and the other partner says no, the no wins. Period. This is not negotiable. If you have a son, your daughter fades further, and if you have yet another girl, you will end up twice as miserable as you are now, and he may start to blame you. (I hope he does realize he determined the gender of your daughter, not you?....)
If he refuses counseling, then YOU should go on your own, right now. Make it happen even if you have to find a sitter for the kids to do it. You can learn some ways to cope with this for yourself and if you are truly considering leaving him over his attitude, you can get the objective advice of a professional. A counselor or therapist also may be able to help you work out how to get your husband into counseling.
Be sure to talk to that professional third party about whether your own perspective might be skewed, too. Can you be objective with yourself about it? Is it possible that maybe your own expectations for how he parents a girl are too high, or just different from what you are seeing in him? I tend to think you're spot on here but it's worth having a third party listen to you and probe whether when you say "in most ways she doesn't have a father" you might have a very different definition of fatherhood than he does. But it would all be better if HE were there to discusss it too....
Have you told him that if he refuses counseling with you, you are seriously reconsidering the entire marriage? Or would he not even respond to an ultimatum like that?
One thing worries me here: you mention in the SWH addition that "maybe there is actually a true man out there" who could love both your kids. Please don't leave just to go seeking another man, for your kids' sake or for any other reason. If you left your husband, do not replace him with another man in hopes of finding that "real daddy" you imagine for your daughter. Just don't. Focus on getting into counseling yourself ASAP and reassessing things.
One other thought: Some men are lousy with babies and toddlers but kind of get into the swing of parenting once a child, boy or girl, is older and the dad can actually talk with and DO things with the child. Is there any chance he's like this? It may be a pipe dream, and don't let this hope keep you hanging on if you find other reasons to leave, but this is worth sitting down and discussing with him now, if you can do it non-judgmentally and he doesn't get defensive about it. "Do you think the problem is really that she's a girl, or is it that she's just a toddler and doesn't really relate to you yet, and you can't do things with her like you can with Son?" This topic is also worth your discussing with a counselor -- though the discussion would be far more useful if dad were there, participating.