I'm not going to financially help my brother move in with a new girlfriend
Why are you not going to help your brother financially? Do you usually help him?
I'm just not going to bother with that since they have been dating for a short time
That is good logic displayed by you because dating for such a short time and already moving in together is a big red flag. However, even if you are rational, I bet your brother will be pissed off and upset that you didn't help him.
I don't care. He's a douche bag anyways.
You have a right to decide what to do but I hope you have a good reason and think it through. It is good to help people when it is the right thing to do.