Your order will remain in Processing UNTIL just before it is being prepared to ship. Your subject says "delivery delay." You are NOT experiencing a delivery delay as Apple clearly told you your order will arrive between October 8 - 14. It's only October 2nd. If you don't get your phone by October 14th, THEN and only THEN do you have an delivery delay.
I know it's difficult to wait for something you want. But when Apple tells you your phone will arrive within the time frame specified, it WILL arrive on time.
When your iPhone is being prepared to ship, the status will update and not a moment before it is being prepared to ship. And once it is being prepared to ship, it will then change to Shipped, and Apple will then send you a tracking confirmation, so you can track it yourself.
You need to patient and trust that things are progressing exactly as they should be.