The critical component of radio astronomy radiometers built to detect redshifted 21 cm signals from Cosmic Dawn is the antenna element. We describe the design and performance of an octave bandwidth cone-disk antenna built to detect this signal in the band 40–90 MHz. The Cosmic Dawn signal is predicted to be wideband spectral feature orders of magnitude weaker than sky and ground radio brightness. Thus, the engineering challenge is to design an antenna at low frequencies, which is able to provide, with high fidelity, the faint cosmological signal, along with the foreground sky, to the receiver. The antenna characteristics must not compromise detection by imprinting any confusing spectral features on the celestial radiation, ground emission, or receiver noise. Innovation in the present design is operating an antenna electrically smaller than half-wave at the highest frequency of operation on the surface of a sufficiently large water body. The homogeneous and high permittivity medium beneath the small cone-disk antenna results in an achromatic beam pattern, high radiation efficiency, and minimum unwanted confusing spectral features. The antenna design was optimized in WIPL-D and FEKO. A prototype was constructed and deployed on a lake to validate its performance with field measurements.