I may be wrong here, but there's no way 13.1 will be ready immediately after the new phones are rolled out. This is an update for later on and I imagine we'll see some more changes to it before it's out. New iPhones will be running one of the betas (without actually being called a beta) as in previous years, and we'll have some update available at launch, but it won't be 13.1.
There will most likely be a 13.0.1 release very shortly after the initial 13 release, and most bug fixes being addressed in the 13.1 betas would be applied in the .0.1 release (save for the omitted “features” we’ll be testing for the 13.1 release).