Shall I review a paper for my advisor?
One way to resolve this would be that your advisor refused to review the manuscript and suggests you as a possible reviewer. Then the editor can decide what to do. Do not overthink why your advisor was chosen first. He has been around for a longer time and is therefore more known to editors. 

I would prefer this procedure to a simple 'yes' to the request  (which would be the easy and probably common approach) because it makes contributions transparent. You made a good start with making yourself the corresponding author of your own paper, so it would be consistent if you sticked to this path.



Addition after comment: The answer above makes most sense if you already know how to handle a paper review resulting in a high quality report. Should you require some general support on this, asking your advisor to do the review together and communicate this accordingly to the editor is a possible and viable alternative.