Final answer:
Davey wants to organize a rally to protest against Pulitzer and unite all the newsies. The rally will take place after working hours to prevent wage loss.
Step-by-step explanation:
The purpose of the rally that Davey wants to organize is to protest against Pulitzer. The rally aims to unite all the newsies and will take place after working hours to prevent wage loss. By organizing the rally after working hours, Davey ensures that newsies from various areas can attend without having to sacrifice their wages.