I'm sorry for your pain, Lilfroggi, it's very hard when a relationship ends 'out of the blue', when you've been given no indication that anything was wrong and there appears to be no concern from your husband about the impact on you and your daughter.
He doesn't want to fix this, he's made a fairly radical decision to move out and he's done it very badly indeed. A decent man would have communicated with you about his unhappiness and given the relationship a chance for both parties to work to sort it out together. He didn't do that.
I don't know if he has somebody else or not. Whether he currently does or doesn't is really not relevant, he's called time on your relationship and done it in a cowardly manner. It's not you, it's HIM. Take some comfort that he (apparently) was not cheating on you whilst in the marital home; it's more respectful (but still cowardly) to move out and make a definite end.
He will still see his daughter and hopefully be a good dad to her if he has been one up to this point. She will be fine; she has you regardless.
I know it's a huge shock for you, Lilfroggi and you will need to take some time to come to terms with it all. You will get over him. At the moment you're sad but anger will replace that and you'll start to feel keen to get him out of your head once and for all. By then he may have realised that he made a mistake but you will be past that and free to make your own decisions for your life from that point forward.
If you have a look at the 'Relationships' board, there's some very good advice there about money and legal matters. There's also a huge amount of kind and honest support there and you'll realise that you're not on your own.
Best wishes to you, Lilfroggi 