Does she make you happy? If you set aside your feelings of being unworthy/undeserving as a partner, would you say that you're happy to be with her? I suggest letting the answer to those questions guide your decision.
If you break up with someone solely because you think that they shouldn't want to be with you, the effect is to rob yourself and the other person of a potentially great relationship.
A PhD doesn't tell you much about someone's personality, a high paying job is something that can be gained or lost, and physical attractiveness is subjective.
If your girlfriend wants to be with you, that makes you worthy/deserving of being her partner. She probably likes you for who you are (which suggests you're probably a better person than you think), and finds you physically attractive (otherwise my guess is that she'd want to just be friends). Chances are that you make her happy, and that she cares more about your personality (e.g. how you treat others, how you think) than about how much money you make or whether you have a degree.