How to convert points to a raster in QGIS (rasterize does not show z field)?

I think the attribute field must be the type Real with a precision of atleast 1. After you saved your points as a shapefile, create a new field using the Field Calculator:

And save it. You should have an attribute table like this:

The new field should now be available for rasterizing:

You could to use "Raster Interpolation" (in Raster menu). Add your data using "Add Delimited Text Layer". (Menu Layer >> Add Layer >> Add Delimited Text Layer.

In Raster Interpolation you could to use Interpolation Method (TIN or IDW), and you could adjust the Cellsize.