Ultraviolet light curves constructed from near-ultraviolet (NUV) and far-ultraviolet (FUV) detectors on GALEX reveal large-amplitude variations during the orbital period of the low accretion rate polar MQ Dra (SDSS J1553+55). This unexpected variation from a UV source is similar to that seen and discussed in the polar EF Eri during its low state of accretion, even though the accretion rate in MQ Dra is an order of magnitude lower than even the low state of EF Eri. The similarity in phasing of the UV and optical light curves in MQ Dra imply a similar location for the source of light. We explore the possibilities of hot spots and cyclotron emission with simple models fit to the UV, optical, and IR light curves of MQ Dra. To match the GALEX light curves with a single-temperature circular hot spot requires different sizes of spots for the NUV and FUV, while a cyclotron model that can produce the optical harmonics with a magnetic field near 60 MG requires multipoles with fields >200 MG to match the UV fluxes.