It seems that she did, unless someone did it for her.
The first entry, or much of it, seems to have been written in pencil first, and then overwritten. Which may not mean anything.
But, if Sophia got a bit confused doing this, it might explain why it says JJ was born Southampton, when that is her birthplace!
Then there is still the other question about the number of children. Four living, when we only know of three.
A very complicated affair, and sorting the 1911 census for the family has been a puzzle in itself!