PRATUSH – Probing ReionizATion of the Universe using Signal from Hydrogen – is a proposed cosmology experiment to detect the global red-shifted 21-cm signal from the Cosmic Dawn and Epoch of Reionization (CD/EoR). PRATUSH orbiting the Moon will seek to precisely measure the low-frequency radio sky-spectrum over 40 to 200 MHz. The scientific observations would be made in the radio-quiet region when in the farside of the Moon, and the data would be transmitted back to Earth when in the near-side. PRATUSH was proposed to the Indian Space Research Organization (ISRO) during a call for proposals in the announcement of opportunity for science payloads in 2018. PRATUSH is in the pre-project studies phase. Here we present a mission concept and baseline design of the proposed payload optimized to operate over the Cosmic Dawn signal band of 55 - 110 MHz. Starting with a description of the fundamental design principles followed, we discuss the PRATUSH baseline design and sensitivity. We further enumerate the challenges that are common to most PRATUSH like experiments, which have been proposed to seek a detection of the CD/EoR signal in orbit in the lunar farside. Due to the highly sensitive nature of the measurement, PRATUSH is designed to operate as a solo experiment with a dedicated spacecraft. Our simulations, assuming a mission lifetime of two years, estimate that PRATUSH would have the sensitivity required to detect the CD signal predicted by the standard models with varying degrees of confidence.A concept model of PRATUSH is under development, which is expected to lead to the engineering model followed by flight model subject to mission approval.