I didn't read the replies.. but here's my advice.
1. Congrats
2. Learn your 5 Cs
3. Read
Premier Diamond and Jewelry Community | PriceScope
4. Go to Spence Diamonds on a slow day and get a crash course on diamonds
5. Buy your diamond online - bluenile, jamesallen, diamondexchange
6. Narrow down 3-4 diamonds you like, bargain
7. Get diamond, get a fake setting or set it on a cheap ring ($500?)
$10-14k budget you are looking at a pretty good diamond (1.1-1.3 carat for above average specs). Don't forget the setting! It's hard unless you know what she likes. They can go $750-$6000 depending on brand, material, design.
Don't bring your real thing to SE Asia. Use a dummy ring.