OP, respectfully, I remember your other post, very recently, about struggling with your daughter starting nursery and how you couldn’t bear being away from her and were dreading her starting school even more and couldn’t cope with the ideas of being away from her that many hours per day five days a week — you need to sort out your own anxiety and depression and what sounds like isolation.
It’s not good for a small child to feel she’s responsible for her mother’s happiness or being her main source of human contact. It’s awful having been bullied in your own schooldays, as I know, but you’re a parent now, and you need to find a way of coming to terms with it, for your daughter as well as yourself, before you start projecting your own insecurities about being disliked onto her. Therapy would help, as it would with your anxiety.
Your DD, to absorb healthy ideas about her own worth, other people, navigating friendships etc, needs to see you modelling confidence in engaging with the world and other people, modelling friendships (does she see you around multiple friends, for instance, doing things with groups or different people?) I had shy, socially-awkward, withdrawn, anxious parents, neither of whom had friends of their own , and my siblings and I absorbed the most unhelpful ideas from them about other people being always more powerful and never to be trusted, and that it was normal to have to run around buying friendships with services. We all spent our later teens and twenties unpicking those scripts. With effort.
The best thing you can do now for your DD is to work on yourself so that you’re modelling healthy relationships, social confidence and that having friendships with multiple people rather than over-relying on one, is a good thing. All the Peppa Pig in the world isn’t going to outweigh what you show her by example. If you start catastrophising about her potentially being bullied or disliked, that’s really not helpful for her. The opposite.
She’s three. At three, my child was still doing parallel play and barely noticed other children unless they took a toy he wanted. He played with different kids every week or two for months if not years after starting school. Lots of children did. For years to come, your DD is likely to be shifting friendships frequently. I don’t think DS’s settled down till he was seven, and then we moved countries so he started all over (and very quickly found a posse in the new place).
But focus on you now. That’s what you can do for your DD.