Convert vector data with irregular points (no grid) to raster with QGIS?

I am aware that how to convert a vector layer to a raster layer is a quite frequent problem and that there are many questions and answers dealing with it. However, none was helpful concerning my specific problem, so I hope it's okay to ask again. I have a huge dataset consisting of fish catch data - different species and the location where they were caught. The original data is a csv file, but I'm working with it in QGIS and have created a vector file from the spreadsheet. Now I want to use another program (Zonation) that only accepts raster files to calculate species richness in certain areas - is there a possibility to create a raster from a vector layer with irregular points? I have tried the Rasterize tool, but it only gives me a solid rectangle and all individual data points are lost. I'm working with CRS WGS 84 and I have tried to set the cell size to 0.4, but still it's only one solid square.