It depends on how you interpret the manga. Gon introduces himself as being almost 12 when he meets Killua, and Killua says "just like me". This could either imply that he's also almost 12, or that he's 12 already. But then during Heaven's arena, he says he was sent there by his father at the age of 6 and was there for 2 years before he reached floor 200, when he was around 8. And when he's there with Zushi and Gon, he says he left 4 years ago. Hunterpedia (HxH wikia) says he's 14, and I personally think he's 14, but it doesn't really matter too much in terms of the series, nor is it really relevant.