Function theory is really designed for adults. When typing children, proceed with caution, especially with the younger ones.
There is a version of the MBTI designed for children called the MMTI-c. (It says it is 98% certain I am an enfp).

But I hsare andy and jennifer's concern that type isnt designed to box children in. Today at lunch it turns out we are using the DISC profiles to make choices about hiring. I find limitation to be disturbing....
My 15 yo ENFP was easily seen as ENP growing up form very early childhood. He was a very clingy, needy infant, would go to anyone, and never, ever sat still. He had endless Ne from very early and was afraid of nothing. If Ne was reined it he would explode in tears and then throw a nightmarish temper tantrum. He was kicked out of five daycares before age five. In second grade we put him on ritalin which helped give him a window of processing time, before exploding...basically by slowing Ne down. Always extremely reactive. At 11, this odd thing happened. His Fi emerged and now he is very sweet and mostly calm.
I cried when I found out I was pregnant again.....
This one is three and he plots against me. When I call him on his strategy, he looks surprised yet pleased. I am a fitting adversary-for a three year old INTJ. At birth he was very clam, quiet, self sufficient, stoic. He hated other people the entire first year. He would glare hatefully at people. Hysterically he really dislikes Fe doms and auxs and says they are "mean" by default. He displays a marked reticent nature in public. He tries on social graces and learns them as Te patterns. He is OCD and quite anal retentive. At 2 he would get really upset if we altered the daily schedule, until I taught him about "special days" which is a category of days, that arent like other days. This all said IXTJ to me, but he plays very strange word games where he swaps names of things for other things. He thinks this is very funny. He says very bizarre things sometimes. My large INTJ says he is a little INTJ.