MAKE and DO are similar in meaning and sometimes hard to choose between.
Generally TO MAKE means (1) to construct, to create, or to form something by putting parts together or combining substances or (2) to bring about, to cause something to exist or come about.
TO DO means to perform an action, or to achieve or complete something.
You MAKE your girlfriend happy means that you cause her to be happy.
You can DO something to make her happy by performing an action that she likes.
In American slang, if you say you DO your girlfriend, it means you have sexual intercourse with her but it has a somewhat vulgar connotation.