I hit reply, and then sat here thinking of what to say...

First off, I don't approve of physical abuse -- whether it's committed by a man or woman. As greggkroodsma (I'll call you gregg for short) posted, we are only hearing one side of the story. And recounting these experiences are NEVER unbiased, no matter how much we try to make them. This isn't a slam to you Zarklon -- this is purely a human fact. We can only relate what we perceive to have happened.
However, with that said, I have no issue with a man restraining a woman who is being physically violent with him (and I'm a woman). As far as I'm concerned, if you are going to hit, don't be surprised if someone hits back. Of course, the stronger the individual, the more restraint they need to learn in responding. (Always a catch, isn't there.) But this isn't the key issue. You're question is basically about how to love again.
This scares me because I know I love this girl
With all due respect, I read that part of your post and went "huh?"
You are out of 2-year, tenuous relationship for only 3 weeks and you *know* you are in love again?!
Maybe the first thing to do is evaluate your definition of love. My sense is what you are feeling is the combination of joy and tenderness you didn't have in your last relationship. This new person is nice and good, as far as you're concerned, and you can't think of why you shouldn't lover her, yet you don't have this energy you equate with love surrounding her. Maybe it's because you aren't in love with her?
I'm not trying to sound trite or blaise, but I don't see how anyone can establish a deep, soul reaching feeling of love for someone else in 3 weeks time. Especially if they are just out of a long-term, bad relationship. And this appears to be your dilemma. Why aren't you feeling the love your head tells you you should feel? The problem is your head doesn't determine love, that's all done by your heart. It tells your brain what's what in this area.
Personally, I think you're moving way too fast. I wouldn't even be dating again for at least 6 months if it were me (actually if it were me, it would probably be more like a year). I think you've been hurt on a number of levels in your last relationship. Before you are capable of feeling that kind of love for someone else, you need to find it within yourself. Only then can you share that with others. And 3 weeks is a blink of the eye when it comes to time. Of course, this could also be a generational difference. The word 'love' doesn't appear to mean the same thing to younger people as it does to me and a lot of my friend.
Of course, this suggestion comes from a much older person (

), but I simply don't think you are ready to make any decision like this right now. Regardless of how wonderful this new girl is, tell her the truth -- You aren't ready for another relationship right now. If she's 'the one', she'll understand and wait for you. If not, then you have your answer. It may sound harsh, but it's the truth -- or I should say it's the truth based on what I've seen over the years.
Hope this helps!