||We study the doped and undoped quantum dimer model using exact diagonalization. In the undoped case, previous studies are consistent with the picture that in the region V/J < 0 the ground state is a spin-Peierls state which is four-fold degenerate. We extend the previous calculation and show convincing evidence that a gap exists between the degenerate ground state and the other excitation states. This is further evidence for the spin-Peierls phase. In the doped model, we search for the existence of a stripe phase where the hole-rich region is anisotropic. We introduce a new dimer-hole correlation function, which can indicate the shape of the hole-rich region. Our results show evidence that the holes tend to cluster together with an anisotropic spatial distribution when the holes are not very mobile. But we do not see strong evidence for the existence of a stripe phase.