You seem to be misunderstanding something. A post-labor has nothing to do with population and everything to do with automation. As it becomes more efficient to have robots and computers to do what was previously human work, we will eventually reach a point where just about every conceivable job that we currently employ people for could be automated.

Most likely, a post-labor world should be capable of arriving well before that. Once we can automate the production of basic necessities, working should become largely optional.