I think the length of time primarily will depend upon a variety of factors including the length of time of the relationship, whether you are the dumper or the dumpee, the circumstances surrounding the break, number of past relationships you may have had, etc.
The emotions one experiences in a divorce are very similar to grief experienced upon the death of a loved one. Which include various stages and one needs to work through those stages to ultimately “get over” it. Plus many people process emotions at varying rates than others.
For me personally, I was the dumpee, it took me about 6 months, we had been married about 15 years. I also highly recommend people see a therapist to help work through the emotions, and determine what you personally did wrong to contribute to the failure of the marriage…it not always just one person’s fault. I didn’t start dating again until about year after the split. We also had 1 kid together who was 6 at the time.