From thread re.
"Politically incorrect national anthems"
The Child's Song We'll sing a song, a children's song, With cheering
rousing chorus, As round our parents' hearths we throng, A safe roof
warm o'er us; Impatient for our coming lives, Awaiting what the
mornings give, Here in the silence of the night, We'll chant a
children's song.
Chorus: Children are we whose lives will flower in
Ireland; Dreaming to free the green land of our homes. We're ...

okay, the lines above are more about being young than about growing up; I found them while looking for Murray McLauchlin'sChild's song (better known from the recording by Tom Rush)
is also at this additional Child's song thread

Charlie McGettigan's Feet of a Dancer (popularised by Maura O'Connell)

for a Bat mitvah, maybe Peggy Seeger's Little Girl Child, though it might have to be adapted slightly for a big girl