because you have been member for at least 1 year when you graduate then you will avoid the normal 1 month quarantine. So it is correct that you can apply for unemployment benefits on the 13rd September, and you will get paid starting from September 14.
And at the same time you should inform your A-kasse that you now have graduated and want to have your status changed from student to graduate.
Finally it is very important that you register as unemployed on Jobnet.dk (or go to your local Jobcenter to do it), also on September 13.
You will only get benefits from the day you are registered as unemployed on Jobnet.dk.
You will receive your first payment on October 1, 2019.
Anders Weber, www.a-kasser.dk