The geometric, spectroscopic, and electronic properties of neutral yttrium-doped gold clusters AunY (n = 1-9) are studied by far-infrared multiple photon dissociation (FIR-MPD) spectroscopy and quantum chemical calculations. Comparison of the observed and calculated vibrational spectra allows the structures of the isomers present in the molecular beam to be determined. Most of the isomers for which the IR spectra agree best with experiment are calculated to be the energetically most stable ones. Attachment of xenon to the AunY cluster can cause changes in the IR spectra, which involve band shifts and band splittings. In some cases symmetry changes, as a result of the attachment of xenon atoms, were also observed. All the AunY clusters considered prefer a low spin state. In contrast to pure gold clusters, which exhibit exclusively planar lowest-energy structures for small sizes, several of the studied species are three-dimensional. This is particularly the case for Au4Y and Au9Y, while for some other sizes (n=5, 8) the 3D structures have an energy similar to that of their 2D counterparts. Several of the lowest-energy structures are quasi-2D, that is, slightly distorted from planar shapes. For all the studied species the Y atom prefers high coordination, which is different from other metal dopants in gold clusters.