If you mean when would you start them for next season, I would say around early March. I'm in a colder zone and I start my peppers indoors in mid-March for planting out in June. You might peruse the Hot Pepper forum to see when others start their seeds.
If you mean how soon can you start them after harvesting, I would say any time, as long as the peppers were ripe when you extracted the seeds. They don't need to be dried for immediate use(they may even germinate sooner than dry seeds), but do need to be dry before storing them for later planting.

Thanks for the help