I think, if possible the children should be tested as soon as possible. Atleast, that way you know what might be coming into play when certain scenario's occur. There is a range of variation in thal (minor)s too. Some have symptoms and some don't. So, knowing about thal(minor) is important even for a children who is 3 or 4 years of age.
In some schools in India, there are non profit organisations who arrange camps and get kindergarteners and primary school kids tested for thal(minor) as there are regions where there is a high precedence of thal. Parents who have kids who are diagonised thal(minor) at such camps are given genetic counselling so that they get themselves tested and are told that if both are thal(minor)s there is a chance of having a thal(major) child.
Unfortunately, in the case above it works the reverse way of getting people aware of thal(minor) but atleast that way, people might think of it. There are millions of undetected carriers and that can be tough for those who don't know what can happen when 2 undiagonised thal(minor)s plan for a child.
As Andy mentioned, it is a good idea to get tested before marriage and/or having a child. As Andy mentions,in the US, there is testing done at birth. Andy, my question is Can they(Gynaec) do the testing when they see the MCV small in size and be proactive? I know the population in US has a low number when it comes to thalassemia compared to the world but with the immigration pattern in US rapidly changing, it might NOT be a bad idea