It depends on how much you want to specialize in general peds without doing an actual fellowship. Every general pediatrician is going to deal with child psych, and they will certainly deal with developmental issues. It's the general pediatrician who usually recognizes that a kid isn't meeting milestones. The general pediatrician is also going to be the first one that parents go to when they're concerned about ADHD, an ASD, and the like. You can always do further study on your own interests. For instance, we have a pediatrician who has made autism and ASDs his own niche, and therefore he has more ASD patients than everyone else in his practice. But another one has made a niche out of breastfeeding and is the go-to person for women with new babies, and yet another is the obesity guy. None of them have done fellowships, but they have studied on their own.
Of course, to really specialize, you have to do a fellowship. Making your own little niche is great, but if you want to be board-certified and an "expert", you have to do the fellowship.
Hope that helps!