'It has been the only time in almost 9 years though, and nothing since. We we're on about 4 hours sleep a night at that point too so I gave some leniency for that.'
OP, I've done shift work for 40 years and had 3 kids, I know sleep deprivation can shorten your temper to like, 5 seconds. When tired to bits, I've snapped, flown off the handle, said things I instantly regretted. But I have never physically attacked my partner and my partner has never physically attacked me. The 'normal' number of physical attacks in a healthy relationship is ZERO. But you know this; my guess is, that's why you didn't mention it at first. It's scary.
I'm sorry, but I think your relationship is hanging by a string. Only you know if your partner is capable of changing, but he's got a huge hill to climb in terms of respect for you and truly sharing in running your household and raising your child.
What on earth is he so scared of? Looking after his own daughter should be a pleasure. Why should you do more, whether housework or childcare? Because you're 'the woman'? 'The mother'? This is the 21st century, for goodness' sake. I agree with the other posters: you would be better off without this constant drain on your self-esteem.
You're worried about breaking up your relationship, but on the evidence you've given, it would be better broken, for both you and your daughter.
I'm not saying that lightly; in general, I think Mumsnet comes to that conclusion a bit too easily. But a man who has taken the liberty of hitting you has stepped across a line; he'll find it much easier to cross it again - and to save this relationship, you're going to be facing him with some hard truths about himself. Can you be sure he won't lash out again when you do?