3 year old won't play with others

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My DD is 3.1 yrs. She has been at nursery since she was 2. Teacher says that all the other kids her age are now playing together, but DD isn't interested. She does her own thing and if one of the other children tries to engage her, she says no and walks away to play by herself.
DD is an only child and has always been surrounded by lots of adults, as we work from home with about 6 staff. She will happily play with an older child or adult, but not kids her age. I try and organise lots of play dates but the other child might as well not really be there, for all the attention DD pays them.
Is this something I should be worried about at this stage? It was long ago that all her peers were parallel playing, but she just doesn't seem to have moved on from that yet.

Hi there. I don't think this is unusual at 3.1. My dd is 3.6 and has only really started playing with others in the last two months. And, when I visit her nursery, there seem to be plenty of children who are happier playing on their own. I think they all just do things in their own time and, like you said, your dd is used to older children whereas my dd finds older children very scary!

DS (nearly 4) is a bit like this too. He still finds big groups tricky and they even held him down at nursery as he found moving into the big group too scary (bless!). He's going up now, and it's because they were brilliant with him, allowed him to find his own confidence and grow at his own rate. Over the past 3 months he's zoomed in self belief, and now quite happily joins in. I don't think he'll ever be part of a gang as it's just not who he is, but he's got the confidence to cope with others now and has started to really make links and friendships with other kids. It's lovely to see, so just wait and I'd bet she'll be the same.

Ds is similar - a tiny bit younger still though.

One thing which I've found helps in those awkward situation when a friend and their child are over at our house and they want to play with ds but he walks off etc. is to do the following:

Get down on the floor and organise some game which you start playing with visiting child and say 'ds/ dd oh we really need you to show x how this works' etc or similar.

It still doesn't mean my ds really interacts that much with the other child but it helps a bit and makes it all a bit less awkward. Plus I hope this will lead to him being more interested in what he can do together with another child.