It's very stressful when our kids have fights, isn't it? As parents, we're focused on keeping them safe and making sure they behave well - and if they have had a fight, they may not have been/done either. And there's not much we can do about it.
It also sounds like you and your husband have different opinions, if he thinks your DD should have hit the other girl, and you don't.
I'd be surprised if school were interested tbh, since the fight happened outside term time and not on school premises.
Good schools take account of major incidents, but this doesn't sound like it was one. They can't possibly police every teenage fall-out - just imagine how many ex best friends, enemies and people each teen doesn't want to sit next to, in a class of 30!
What's more, you did not see what happened: you can't say for sure that your DD 'was attacked'. And I know from experience that our own DCs can be rather unreliable witnesses - not (or not only) because they tell us what they think we want to hear, but also because different people have different perspectives, especially in an argument. With only your DD's version of events, I'm afraid you run the risk of complaining about this girl, and then discovering your DD attacked her, or hurt her more badly than she hurt your DD.
I think what you do next depends on how well you know the other girl's mum, and how sure you are that this was 'a minor incident'. If you know her and are sure she'll be reasonable, speak to her. If you think there may be more to this than meets the eye, also try to speak to her. Otherwise, it's probably best to just let it go.
It might be a good idea for you and your husband to discuss and agree what you want your daughter to learn about resolving conflict. At the moment it sounds like your DH has given your DD the message that it's ok to fight and hit people, under certain circumstances... Is that what you want her to learn?