Consider a $P^1$ with effective orbifold structure at $0$ and $\infty$.  We show that that the equivariant Gromov-Witten theory of such an orbifold is governed by the 2-Toda hierarchy. The proof follows that of Okounkov and Pandharipande for the case of a smooth $P^1$, and goes through Hurwitz numbers and the representation theory of the symmetric group. In the case of an ineffective orbifold, the Gromov-Witten theory is governed by commuting copies of the 2-Toda hierarchy, and the symmetric group is replaced by wreath products.