The Radio Frequency Quadrupole of SANAEM Project Prometheus will be a demonstration and educational machine which will accelerate protons from 20 keV to 1.5 MeV. The project is funded by Turkish Atomic Energy Authority and it will be located at Saraykoy Nuclear Research and Training Center in Ankara. The SPP beamline consists of a multi-cusp H+ ion source, a Low Energy Beam Transport line and a four-vane RFQ operating at 352.2 MHz. The design studies for the multi-cusp ion source (RF or DC) were performed with IBSimu and SIMION software packages. The source has already been produced and currently undergoes extensive testing. There is also a preliminary design for the solenoid based LEBT, POISSON and PATH were used in parallel for the preliminary design. Two solenoid magnets are produced following this design. The RFQ design was made using LIDOS.RFQ.Designer and it was crosschecked with a home-grown software package, DEMIRCI. The initial beam dynamics studies have been performed with both LIDOS and TOUTATIS. This paper discusses the design of the SPP beamline focusing on the RFQ beam dynamics.