Blazars have traditionally been separated into two broad categories based on their optical emission characteristics. Blazars with faint or no emission lines are referred to as BL Lacertae objects (BL Lacs), and blazars with prominent, broad emission lines are commonly referred to as flat-spectrum radio quasars (FSRQs). The spectral energy distribution of FSRQs has generally been thought of as being more akin to the low-peaked BL Lacs, which exhibit a peak in the infrared region of the spectrum, as opposed to high-peaked BL Lacs (HBLs), which exhibit a peak in UV/X-ray region of the spectrum. All blazars that are currently confirmed as sources of TeV emission fall into the HBL category. Recent surveys have found several FSRQs that exhibit spectral properties, particularly the synchrotron peak frequency, similar to HBLs. These objects are potential sources of TeV emission according to several models of blazar jet emission and the evolution of blazars. Measurements of TeV flux or flux upper limits could impact existing theories explaining the links between different blazar types and could have a significant impact on our understanding of the nature of objects that are capable of TeV emission. In particular, the presence (or absence) of TeV emission from FSRQs could confirm (or cast doubt on) recent evolutionary models that expect intermediate objects in a transitional state between FSRQ and BL Lac. The Whipple 10 m imaging air Cerenkov gamma-ray telescope is well suited for TeV gamma-ray observations. Using the Whipple telescope, we have taken data on a small selection of nearby (z < 0.1 in most cases) high-peaked FSRQs. Although one of the objects, B2 0321+33, showed marginal evidence of flaring, no significant emission was detected. The implications of this paucity of emission and the derived upper limits are discussed.