I taught overseas for 11 years (and loved it!)

- in the Philippines, Turkey, Japan and Latvia. In international schools where the language of instruction was English, but the kids were from all over the world - their parents were either international business people, embassy workers, military, super rich from the host country, or other teachers' kids.
I'd be happy to answer any questions you have about teaching overseas and how to get jobs overseas - pm me with questions about working overseas.
Most of the major job fairs are held in January or February, so now is actually a good time to get started in the process of looking. Start by looking at
TIE it is an online newspaper for international teachers - it includes articles by teachers overseas as well as lists job services and positions available.
As far as how schools would be for a gifted kid..... Most of the schools I know of do not have any services for kids at either end of the spectrum. Living in another country is such an exciting and interesting lifestyle change that there is a lot to "keep a kid interested in", but in terms of actual programs at a school that are good for gt kids it will limit your choices. Even the really good schools I am familiar with are not set up to deal with HG/PG kids.
How old are your kids again? Many of the schools do the IB (International baccalaureate) program at all levels, some do their own curriculum in all levels based on the country their administrators are from, and others do the international version of the British system (IGCSE and A levels for high school).
But, as I said, immersing yourself in the culture you are living in and learning the language and discovering as much as you can about the area may make up for what is lacking during the school day. It certainly opens your eyes to life outside the US, as well as to life in the US.
DH and I loved working overseas, DD7 was born overseas and we will go back out again in a few years because we loved it so much. We also really want both DDs to get a chance to live abroad again when they are old enough to remember it.