The origins of life on Earth have been the subject of inquiry since the early days of philosophical thought and are still intensively investigated by the researchers around the world. One of the theories explaining the life emergence, that gained the most attention recently is the RNA World hypothesis, which assumes that life on Earth was sparked by replicating RNA chains. Since wet lab analysis is time-consuming, many mathematical and computational approaches have been proposed that try to explain the origins of life. Recently proposed one, based on the work by Takeuchi and Hogeweg, addresses the problem of interplay between RNA replicases and RNA parasitic species, which is crucial for understanding the first steps of prebiotic evolution. In this paper, the aforementioned model has been extended and modified by introducing RNA sequence (structure) information and mutation rate close to real one. It allowed to observe the simple evolution mechanisms, which could have led to the more complicated systems and eventually, to the formation of the first cells. The main goal of this study was to determine the conditions that allowed the spontaneous emergence and evolution of the prebiotic replicases equipped with simple functional domains within a large population. Here we show that polymerase ribozymes could have appeared randomly and then quickly started to copy themselves in order for the system to reach equilibrium. It has been shown that evolutionary selection works even in the simplest systems.