There is no GST for fine precious metals in New Zealand. Gold with a fineness of not less than 99.5%, silver with a fineness of not less than 99.9% and platinum with a fineness of not less than 99% are exempt from GST. The GST is a tax on the taxable delivery of goods and services in Singapore and on the import of goods into Singapore (except for an exempt import). This means that the GST applies to all products that are brought to Singapore or purchased locally.
As with all purchases, you'll have to pay a 7% GST for your ring.