The beginning of the novel shows that the Darlings are poor and Mr. Darling absurdly cares more about keeping up with his neighbors and maintaining appearances - to the point that he hires a dog for a nurse rather than not have one. Mrs. Darling loves her children and as the "custom of every good mother" she puts them to bed and replaces their naughty thoughts with good ones. Peter Pan enjoys secretly flying to the Darlings' window and listening to Mrs. Darling tell stories to her three children, Wendy, Michael, and Jon. He decides he wants a mother and sprinkles fairy dust on the three Darling kids so Wendy can fulfill the roll in Neverland.
Tinkerbell, a fairy, likes Peter Pan and is jealous of his fascination with Wendy. She tries to get the lost boys to shoot Wendy with arrows as she arrives in the magical place of Neverland. Wendy lives and pretends to be a mom to the boys tucking them in at night and reading stories. Meanwhile, the evil but buffoonish Captain Hook is bent on kidnapping Wendy for himself and his crew of pirates. He wants a mother too. He succeeds until Peter Pan rescues Wendy and battles Captain Hook. Wendy and her brothers return to their parents and she returns to Neverland to do spring cleaning for Peter Pan until he forgets about her.
In a scene where George is being hypocritical toward his son that doesn't want to take medicine, he takes it out on Nana by refusing to let her sleep in the kids room. Nana spends the nights in the three kids bedroom because Mrs. Darling knows that it protects them from Peter Pan. When Wendy hugs Nana to prevent him from putting her in the doghouse, George yells about not getting any attention. George "craves admiration" and wants to be known. In an ironic twist, George eventually gets media attention when he decides to sleep in Nana's doghouse until the missing children are found.
I found the Victorian narrator slowed down the pace and was irritating, but it is what gives the satirical tone. Peter Pan represents Romanticism and Barrie's desire for a simple past. Peter Pan is cocky and selfish, who doesn't want to grow up nor have responsibilities. Wendy is in love with him but he is incapable of loving anyone but himself. His pretend world is his reality where "lovely thoughts" are the impetus for flying. He is asexual and refuses to constrain his imagination, getting whatever he wants, and not connected to any love for other people or fairies. In this context Barrie subverts the notion of childhood as a way to attack common adult values and conventions. Peter Pan is a happy uncivilized anarchist and paradoxically admired and good. I like the odd Victorian writers, but this was not a favorite mainly because of the narrator. You'll have to decide for yourself.
By the way, Artur Rackham's gorgeous illustrations are in this edition.