I just feel she doesn't need to be sent off to nursery at 3 in a class of 25 or so with a couple of teachers, probably getting less out of being there than she would being at home or at groups with me for a little while longer.
That's very negative OP.
I felt the same as you three years ago when my DS1 was due to start pre-school aged 3. I am a SAHM and did wonder about sending him.
However, a lot of posters think this is "handing him over" to state education, when in my son's case, it was 9am til 11.30 am in term time. We still had days out and went to the park and met friends etc.
However, he completely loved his pre school, which luckily was based in the school he now attends. He is still friends with kids he met there, and I am friends with their mothers too.
It was not demanding and the wonderful teacher was very well supported with about 6 amazing TAs. They did painting, colours, circle time, learnt songs, had a snack and came home again. At Christmas, they did a nativity play that I still treasure the memories of.
I can do so many things with him, but I am not kids his own age, and I cannot teach him how to behave in class of 25 other kids. Nursery/pre school did this and the pleasure it gave him outweighed any initial doubts I had. It also taught him to emulate his peers, which can only be a good thing.
I am not telling you what to do OP, but give some thought to the positive side. I'm glad I did, the rewards were manifold.