According to the theory on personality page, kids aged between 7 and 12 have developed three out of four preferences (meaning their dominant function is defined but the auxiliary is not), while younger children have just two letters, i.e. they can can be EP, EJ, IP or IJ. Though I suppose that, if this were true, the speed of developing preferences could vary greatly according to the way a certain child develops in general. So perhaps one very young child could have all four preferences developed, while another child of the same age cannot be typed at all because his/her preferences haven't stabilised yet.
In any case, the test on this page and the theory behind it works for me, I gave it to both my parents to solve and in both cases I came out an EFJ child