Half-integral weight modular forms give rise to automorphic forms on the metaplectic cover of GL(2,A) -- a central extension by \mu_2. For an odd prime p, we consider the corresponding covering of GL(2,Qp) and study its smooth mod-p representation theory as well as its relation to Galois representations. This contains the well-known mod-p local Langlands correspondence for GL(2,Qp), part of which we will review, but is new for the so-called genuine representations (i.e. \mu_2 acts via the non-trivial character). This includes a complete classification result of the smooth irreducible genuine mod-p representations.