Wittgenstein's Private Language Argument contends that it is impossible for one to form a language by oneself. Here's a counterexample. You live on an island that has no people other than yourself. You live for forty years there. Then you step in a time machine that was left there by someone else. You go back forty years. You do this 999 times. (Let's assume that the time machine also fixes up your body so you can live for a subjective length of 40000 years.) To an outsider, the island looks populated by a thousand people of remarkably similar appearance. There is a community there. But that community in fact includes only one person, you. So, it's possible to have a community with only one person. But there is no reason why such a community couldn't develop a language, since it functions just like all other communities do.
A fun question: Suppose Marcy and George join you on the island, but they don't do any time travel, and so there you are located in 1000 places on the island, and then there is Marcy and there is George. In elections, should you get 1000 votes, with each of them getting only one—there does, after all, seem to be a sense in which you have a lot more interests—or should each of the three people on the island get exactly one vote?
By the way, the clip below illustrates the wrong way of imagining the scenario. In my scenario, it is a mistake to think of first the island having you in one place, then of it having you in two places, and so on. Over the 40 year period in my scenario, you always are in 1000 places.