Answer by Japanese teacher
In general, it is not recommended to ask for someone’s age in Japan because it is not considered a very polite thing to do. However, if you must, and if the situation allows you to do so, such as in this case, you can say oikutsu desuka. This is a polite way of asking someone’s age. To ask the age of a child, you can drop the honorific o, and ask “ikutsu?”
Nansai desuka is usually used when you are asking about the age of a third person. For example, “anohito wa nansai desu ka” (how old is that person?). It is less polite than oikutsu desuka and thus should not be used to ask for someone’s age directly.