Can a cloned animal have babies?

Can identical twins have babies? Yes.

A cloned animal, except for its age, is indistinguishable from an identical twin. Depending upon how it was cloned, the telomeres of its DNA may be shortened, but this would have little impact on its ability to breed.

In short, yes, cloned animals may have babies, and live out their lives as naturally as uncloned organisms, and this has been demonstrated in numerous cloned species.