The way I see it, Moore's argument gets you to where you're uncertain of the reasoning pro or contra skepticism. But If you start from the position of epistemic solipsism (I know my own mind, but I'm uncertain of the external world), then you have reason (more or less depending how uncertain you are) to side with common sense. However, if you start at metaphysical solipsism (I'm uncertain of my own mind), then such an argument could even be reason to not side with common sense (e.g., there are little people in my mind trying to manipulate my beliefs; I must not allow them to).