Is your analysis based on "freudian psychoanalysis" or just "psychoanalysis in general" ?
If it is the latter, then you'd have to go with what Lacan said about the father figure, that it isn't always the biological one, and that there always is a father figure, who would that be in Rorschach's case ? Not. A. Fucking. Clue.
Father figures: President Truman. Comedian.
He seeks to avenge the Comedian. By avenging, he puts himself in the Hamlet position, ergo Comedian = father figure whose mantle he wishes to inherit. What troubles Rorschach seems not to trouble Comedian, a condition to be admired by Rorschach. Hence his shock when he discovers Comedian showed weakness to Moloch. etc.
In terms of father figure / home life he substitutes Dan Dreiberg and the Nite Owl Cave.