Laughalot - hopefully you are already assured by this thread that your DD is perfectly normal and the old dear teacher is wrong. Clearly she's quite old school. I would have been at nursery in her 'prime' and could write etc at that age - it was the norm. Now not so.
My friends DS was not at all interested in anything other than tractors, even playing outside he had to take a tractor with him!
He chose to play with the tractors instead of paint/storytime/playdoh/messy play/sticking/cooking/anything and really had to be badgered into doing anything else... he had no idea about any letters/numbers anything and absolutely zero interest...and his speech was terrible.
We were all starting to get worried about him, both from a 'is this normal' viewpoint and a htf is he going to get on at school where he has to do certain things.
Well, he started school in September and hasn't looked back! He still can't write his name, but he does attempt it when he has to [bgrin], he brings home 'stuff' (one painting from all his time in nursery! lol) he still loves tractors... but his teacher says he's a pleasure to have, really knowledgeable about all kinds of things (takes after his Dad, quiet but a mine of info!), he will happily speak in front of the whole class etc.
His speech is still quite difficult to understand at times, but his teacher said no more so than a handful of others in the class and it is improving.
Yesterday he joined in some board games with us, was able to recognise numbers, letters and follow the rules - it was quite astounding how quietly different he has become in such a short time! He is loving school.
I would ask the nursery to assign a different key worker to her myself or if its the entire nursery, move her to a different one - they soon make new friends at that age.