Whilst the 1939 register as it stands at the moment contains 41 million names of which just under 33 million are available, it is a one date snap shot, 29th September.
This register was primarily used to issue identity cards on the outbreak of war in 1939.
It did not include those who had already signed up, those who lived outside of England & Wales and potentially those away on holiday as it was taken during September.
Anyone who was born after that date, or who arrived in the country after that date was listed in a separate register which is not publically available.
If they weren't registered to start with, they certainly would be by January 1940 when rationing started.
If the date on the death entry is consistent with the date on her birth cert and baptism entry, then you can do a 1939 search just on that information and look throught the 2272 results to see if she is potentially mis-transcribed.
I'm having trouble locating the school entry you mention, which dataset are you referring to and what address is actually given on the register
