My son is very close in age to your DD. At this age they really just need to potter about with their main caregiver/usually mum. They don't really play together at this age and she is young enough that the dominant idea and drive in her mind is to make sure she stays pretty close to mum! Everything else is secondary.
At some point, perhaps between 3 and 4, you will prob notice that that is no longer the all encompassing drive of your DDs life - she will have matured enough to know that she can be apart from you and that you will return, she can understand time concepts better. At that point her mind is freed up from the context attachment issue, so that she can really get involved in playing imaginatively and pottering around (by herself) and also forging friendships. I noticed with my DD that it was at some point after 3 that her friends really began to mean a lot to her in the kind of way that our friends matter to us. Before that, other children were around and sometimes interesting, but she didn't have a relationship with them as such.
That's not to say they can't form relationships at around 2 - my son has a little friend we see a lot of, he knows her name, he blows her kisses. But he doesnt play with her as such, nor does he have a "friendship" with her. I suspect in a years time though, we might start to see that developing.
So I would say you have got a year or so to find your feet before you perhaps have to make yourself find friends for your DD.
Ive taken my son to various activities this week to try them out, but my overwhelming conclusion is that he is too young at nearly 23 months. Toddler activities like football, gymnastics, art clubs are hard work even if you don't have PND and are a naturally outgoing type, because you have to try and cajole them into doing the activity and fitting in with the class, not easy at this age. I think I am going to leave most of the activities for the moment and just potter about with my son and have coffee with friends. When he is three, he will be much more suited to classes.
I would start with something like a toddler group, where your DD can hopefully just play at your feet and you can have a coffee and chat. You could then invite a nice mum out for a coffee or round to yours to play with their child.
Good luck.