Update (10:30 AM): After more than 10 hours, orders for the gold version of the iPhone 5S on the online Apple Store (Singapore) can no longer be placed. Instead, it's now listed as 'unavailable'. The white/silver and black/grey versions still list an October shipping time frame. Elsewhere, in China and Australia, the gold iPhone 5S is listed to ship in October; the other colors in 7 to 10 days.
On the other hand, the iPhone 5C (all colors and capacities) is available to ship in 1 to 3 business days, which is a sign of ample supply.
The Apple Online Store (Singapore) just went live a few minutes ago, but it seems that the overwhelming global demand for the iPhone 5S has caused its shipment date to be pushed to October.
At point of publication, the website states the shipment date of all the iPhone 5S models (three colors and three storage capacities) to be in October. Its polycarbonate counterpart, the iPhone 5C, appears to be sufficiently stocked, as the delivery date is still stated as 20 September (today).
Just a few hours ago, we dropped by two telcos' outlets and an Apple authorized retailer (EpiCentre) where the turnout was considered smaller compared to previous years. This was mainly due to better organization on the part of the telcos, where pre-registered customers of SingTel and StarHub were allocated time slots to purchase their devices.