I have some data as .shp (polygone representing Antarctica continent). I would like to know if there is a way to create a raster containing the lat/lon for each grid point ... Has somebody here tried to to that?
Based on your description above, you have a polygon layer (not a raster). You can easily make a regular grid covering that polygon with the QGIS tool "Vector->Research Tools->Vector Grid". Then, as GISJohnECS explained, you can get the centroids of each grid cell. This will create a third vector points layer. Finally, open the Field Calculator for this point layer, and use the geometry functions $x and $y to add two columns for longitude and latitude. You can read some more details in the QGIS documentation. That will give you all the long/lats of each centroid of all the cells in your (vector) polygon grid.
However, can I suggest you explain what it is you're trying to do?
Perhaps add more detail to your question, a preview of your .shp file would be nice. Assuming your .shp is a polygon of Antarctica divided into grids, and you want the Lat/Lon of each grid, to convert into a raster, Use the Go to the menu -> Vector -> Geometry tools -> polygon centroid and create a centroid point layer.
And then use the Interpolation Plugin to convert your centroid file to a Raster, using whatever attribute value you wish. If the attribute value from your polygon file is not attributed to your Centroid Output, just use a spatial join
Adding on based on your comment, Micha has added an answer assuming you just meant you wanted the XY values from a vector grid, but, assuming you want XY values from a raster, here is my take from this Tutorial use the Regular points Tool found in Vector->Research Tools-> Regular Points this tool will get regular points in a grid format separated by a defined distance, if you want points in each grid you can try define the distance as the width of each pixel understand if you have a high resolution raster it may crash, normally I just define a number of points like 100000 or something
This will give you X,Y locations of each point that was generated, that may not be from each pixel though... As i mentioned this assumes you really want the XY values for pixels... But also read Michas Answer to see if thats what you wanted