Quantum optical coherence tomography (QOCT) was proposed some time ago as a highly promising alternative to its classical counterpart for obtaining morphological information of semi-transparent, e.g. biological, samples. In particular, since the time when QOCT was first proposed two key advantages were identified with respect to an equivalent classical system: even-order dispersion cancellation in the sample under study, as well as a factor-of-two improvement in axial resolution. However, the low-flux nature of photon pair sources and the resulting long times of data acquisition, have severely limited the practical applicability of QOCT. Our present work aims to overcome some of these limitations through the implementation of a Fourier domain version of the technique which eliminates the need for axial scanning.