The quantum photodynamics of a simple diatomic molecule with a permanent dipole immersed within an optical cavity containing a quantized radiation field is studied in detail. The chosen molecule under study, lithium fluoride (LiF), is characterized by the presence of an avoided crossing between the two lowest 11 potential energy curves (covalent-ionic diabatic crossing). Without field, after prompt excitation from the ground state 1 (1)Sigma, the excited nuclear wave packet moves back and forth in the upper 2 (1)Sigma state, but in the proximity of the avoided crossing, the nonadiabatic coupling transfers part of the nuclear wave packet to the lower 1 (1)Sigma state, which eventually leads to dissociation. The quantized field of a cavity also induces an additional light crossing in the modified dressed potential energy curves with similar transfer properties. To understand the entangled photonic-nuclear dynamics, we solve the time-dependent Schrodinger equation by using the multiconfigurational time-dependent Hartree method (MCTDH). The single mode quantized field of the cavity is represented in the coordinate space instead of in the Fock space, which allows us to deal with the field as an additional vibrational mode within the MCTDH procedure on equal footing. We prepare the cavity with different quantum states of light, namely, Fock states, coherent states, and squeezed coherent states. Our results reveal pure quantum light effects on the molecular photodynamics and the dissociation yields of LiF, which are quite different from the light undressed case and which cannot be described in general by a semiclassical approach using classical electromagnetic fields.