Goodness, your girl sounds identical to me when I was that age.
Is she an only child? (I am).
I can only speak from my experience, which may or may not relate to your DD. In my experience, children could be very cruel to me, but I didn't realise how flippant children can be, also. As an incredibly sensitive individual, I've had to develop a tough 'outer skin' in order to prevent taking every comment to heart (I'm just 30yo now).
So, a child would say something unkind to me, it would wound me; break my little heart and it would take me ages to recover. Meanwhile, because I was hurt, I'd cry easily, probably wasn't much fun to be friends with and so would be left out.
I was bullied ... perhaps your DD is, too? You need to establish whether this is the case and tackle it head on, immediately if it is the case. Bullying did great damage to my already fragile self-esteem which contributed to issues I had later in my teens-mid 20s.
I felt 'safe' when in the company of a few, very trusted, friends. KB, KH and JG were girls who were never mean to me and inherently understood my gentle nature. My Mum included them (particularly JG) in many aspects of my out-of-school-life: sleepiness, days out and the like. This was an excellent strategy. I'm still in touch with KB to this day.
You seem to be tuning in to your DDs needs - stay vigilant, let her talk, don't judge or get cross (if she's anything like me, this would be internalized) and with the best will, you will sort this out together.
Good luck x