Laura definitely shows signs of super ego, she has a moral core, especially when it comes to her relationship with her brother. She reminds him that their mother should be respected. Laura has more of a conscience than Tom does.
"The superego represents the conscience and values an individual acquires from parents and society."
In Scene Four, Laura beseeches her brother to make up with their mother. She begs him:
"Tom, speak to Mother this morning. Make up with her apologize, speak to her." (Williams)
It makes Laura very uncomfortable when Tom and Amanda fight. Although Tom may have cause to react to his mother's constant direction on how to live, Laura takes a softer approach. She respects her mother even though she also experiences her criticism.
Laura does not want to present herself as false in any way. When Amanda puts the "Gay Deceivers" into her dress, telling her that she should enhance her figure, Laura takes them out, refusing to compromise her integrity. Laura may be shy and unassuming, but she is more honest than the other characters.
Laura is more authentic than either Tom, Amanda or Jim. She has a more responsible conscience than Jim, who flirts with her, leads her on, kisses her and then drops a bomb on her, telling her that he is engaged to be married very soon.
I would say that Laura does not exhibit any signs of having a conscience or moral compass because of the nature of her character as she is developed in the play. Laura's personality is so fragile--actually fractured--she does not interact with the world or with others in any authentic way. She moves through her very small world as the shadow of the person she might have been but did not become. Simply, Laura exhibits no displays of conscience because she takes no actions that she herself would review or judge in moral terms; she does nothing to provoke her own conscience.
The only thing Laura does that might suggest a display of conscience is covering up the fact that she dropped out of business school. An argument might be made that she felt ashamed because she knew her mother had paid for her to take the class. However, other arguments could be made that Laura kept this secret because she feared her mother's reaction and because she was ashamed not for what she had done but for what she perceived herself to be.
Laura does not show any signs of a super ego, she is a very humble person.