I'm certainly no expert by far since I have no kids- so feel free to ignore me completely
but - I will tell you the experience of my sister
My sister's (step)son, now age 7 and in the second grade, didn't go to nursery school at all- (they couldn't afford private pre-school and there was no headstart in their area). She brought him to story hour at the library and worked with him on his academics, did cooking for teaching maths, etc. He was fine academically- in line with the other kids, etc. He didn't have seperation anxiety or anything going to kindergarten, he was quite willing and able to go, he loved going! However, the one thing he really struggled with was "how school works" i.e standing in lines, raising his hand (he did have some of this in story hour), waiting to be called on ,calling teachers properly, actually using the toliet with other boys around instead of just playing, etc. My sister did have her hands full in kindergarten and first grade and he needed behaviour charts, etc for doing schoolwork and not playing, not acting out, listening, paying attention, not talking when he's not supposed to, etc - However, he's doing much better now in the second grade.
Now, I know most of that is down to her son's personality- but she does wish that she could have gotten him into school sooner- and now that her other son is 2.5 and almost potty trained, she's ready to push him into preschool as soon as he's able to go (she moved to a new area with headstart)- So its worth considering these things with your daughter when trying to weigh the pros-and cons. However, I think like anything else parenting is a very personal process, (which again, I have no experience of, so just ignore me!!!
) so you need to do what ultimately you think will be best for your kiddo.