Hey there! I'm a PRS-T1 owner from Singapore, and very happy with the reader so far.
To answer you question. There isn't a Sony Store in Singapore, so you can't purchase ebooks the Reader Store unless you have a credit card with a US billing address. That's how I managed to work around it the one time I bought from the Store. However, as others have said, there's absolutely no reason to purchase from Sony when there are plenty of other online stores with pretty good selections. Kobo's store doesn't have any geographic restrictions and offers decent discounts every so often.
And in Singapore, there's Singtel's Skoob bookstore:
http://www.skoob.com.sg. The range is obviously not as wide as Amazon or B&N etc., but I've found a few buys that are around 20% cheaper than the prices at Amazon or Kobo. You just have to close one eye to Skoob's ignorance of e-readers in their technical support section. They seem to think that everyone reads ebooks on a mobile phone! There isn't even a mention of the format of their ebooks, which is EPUB-DRM, by the way. They work just fine with the PRS-T1.