My mother is a piano teacher.
I participated in competitions when I was in high school (second place in my age group in my state, woo-hoo!).
My son plays piano.
He has participated in one "concert-competition" so far (arranged by my mother, not by his piano teacher)
The above was just background for where I'm coming from.
IMHO, if your teacher thinks your child should start music competitions, then s/he thinks that your child can do them at whatever practicing level s/he is doing now, so absolutely don't worry about it!
I personally (and I think the same is true for my son) LOVED performing, competing, showing off, etc. I was not a big fan of practicing and only practiced when I had the incentive of a concert/competition coming up.
When I was very young (i.e., elementary school) I did not get stressed out at all. I'm pretty sure my 8-yer-old does not. He certainly does better at his concerts than at his lessons and does not seem particularly worried. As I got older, I would get more worried (i.e., jittery, butterflies, etc), but I still enjoyed performing.