This is a children’s picture book I read in the 1980’s. The protagonist “despises” (I think she uses that word) a mean girl/bully. In the end I think she discovers that the bully doesn’t have any friends and is sad, and would like to be the protagonist’s friend. There is also a cupcake (it might have a candle on it). I think the bully gives it to the protagonist to try and make friends but the protagonist is suspicious of it and wonders if it’s poisoned. The bully wears a frilly dress. I think at one point she has a lollipop.