Well, as GrandFather pointed out, there isn't anything that one language can do, that another can't. The exercise reduces to proving Turing's Halting Problem, which Turing already proved. So yes, your original idea is OK - Perl can do whatever any other language can do. We've known this for something like seventy years (except, of course, Perl hasn't exited all that time).
UPDATE: As Tilly has pointed out, this has nothing to do with Turing's Halting Problem. It has to do with Church's Thesis (thank you, Tilly, for correcting me).