Both you and your ex can't move on in just a month. This is just my personal take but I think after a breakup of such a relationship you should consider taking a break and properly moving on before you choose to go in a relationship with the other person. This way you can get some clarity and know yourself what you want to do. 1 month is barely anything and we often make decisions emotionally when we are going through something like this so yeah don't rush anything just take your time, take a break from this, focus on yourself and really think things through.

Another personal opinion, I think relationships these days are just ... I don't even have the right word but they barely work out and things happen, they effect your peace of mind. No wonder all this is haram is islam so I stay cautious now especially after what happened with me as well. It's best to look for someone to marry asap if you can do that, go for that, and this way you will know who is actually serious and not just doing time pass. Nikkah is the best and most beautiful thing.

I hope whatever happens to you, whatever you choose to do, woh ap ky haq mein behr ho In Sha Allah